jgsugden
Legend
They work how each ability says they work. Each ability is written differently. Where it is unclear, it is up to the DM.
Great Old One Warlock, Awakened Mind:
You can telepathically speak to any creature you can see within 30 feet of you. You don’t need to share a language with the creature for it to understand your telepathic utterances, but the creature must be able to understand at least one language.
This one allows you to speak to, but not receive messages from, a target creature within 30 feet (confirmed in Sage Advice). As long as it understands a language, it can understand you, and anything you can do in speech you can do in this telepathic one way conversation (yell, whisper, modulate your mental voice, etc...). There is nothing to indicate that the target will know the source of the speech if you do not identify yourself, so whether they do or not is up to the DM (unless you identify yourself in the communication). You must be able to see the creature to use the ability.
I had a Circle of the Moon Druid PC in a game that took one level of Great Old One Warlock (making a Pact with an alien nature spirit). Hex (which it could redirect while wildshaped), Armor of Agathys (not concentration and is nasty with high level druid spell slots) and Awakened Mind were iconic elements of his combat identity - a very efficient, evocative and creepy PC.
A telepathic monster doesn’t need to see a contacted creature and can end the telepathic contact at any time. The contact is broken as soon as the two creatures are no longer within range of each other or if the telepathic monster contacts a different creature within range. A telepathic monster can initiate or terminate a telepathic conversation without using an action, but while the monster is incapacitated, it can’t initiate telepathic contact, and any current contact is terminated.
A creature within the area of an antimagic field or in any other location where magic doesn’t function can’t send or receive telepathic messages.
You do not need to see the target (although they must stay in range), it is two way communication, and once initiated it can continue so long as they stay in range (as specified in the ability). This ne is not labeled as "you speak", so a DM might rule that changes of inflection and volume are not possible here - that the telepathy here is not capable of the modulations we have in speech.
Telepathic Bond Spell
You forge a telepathic link among up to eight willing creatures of your choice within range, psychically linking each creature to all the others for the duration. Creatures with Intelligence scores of 2 or less aren’t affected by this spell.
Until the spell ends, the targets can communicate telepathically through the bond whether or not they have a common language. The communication is possible over any distance, though it can’t extend to other planes of existence.
This is a far reaching communication that is not limited by range, but as it lacks that "speak" language, the DM may say that inflection and volume changes are not possible. This does not require a common language, or any language at all (so long as they have intelligence 2), so it is quite more versatile than the previously discussed forms. It is also not necessarily clear who the speaker is amongst those involved in the circle. All of that is up to the DM. Minimum Intelligence 2.
Early in 5E I played a Great Old One Warlock. He was pact of the Tome, and he used this spell with the party all the time despite having the Awakened Mind ability. They each had advantages that the other lacked.
Telepathy Spell
You create a telepathic link between yourself and a willing creature with which you are familiar. The creature can be anywhere on the same plane of existence as you. The spell ends if you or the target are no longer on the same plane.
Until the spell ends, you and the target can instantaneously share words, images, sounds, and other sensory messages with one another through the link, and the target recognizes you as the creature it is communicating with. The spell enables a creature with an Intelligence score of at least 1 to understand the meaning of your words and take in the scope of any sensory messages you send to it.
Longer duration, allows communication with a creature of intelligence 1, and you can transmit more than words.
Telepathic (Feat - UA)
You can speak telepathically to any creature you can see within 30 feet of you. Your telepathic utterances are in a language you know, and the creature understands you only if it knows that language. Your communication doesn’t give the creature the ability to respond to you telepathically.
Very similar to Awakend Mind, you get to speak and it is one way communication.
Enhanced Find Familiar Telepathic Bond
The [familiar] can serve another creature as a familiar, forming a magic, telepathic bond with that willing companion. While the two are bonded, the companion can sense what the pseudodragon senses as long as they are within 1 mile of each other. While the [familiar] is within 10 feet of its companion, the companion shares the pseudodragon’s Magic Resistance trait. At any time and for any reason, the [familiar] can end its service as a familiar, ending the telepathic bond.
There are no words exchanged, just senses, with an enhanced familiar.
Find Familiar
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has. During this time, you are deaf and blind with regard to your own senses.
This one is ambiguous in a key regard - the "During this time" statement could apply to only when you see and hear through the familiar, or any time you communicate with the familiar telepathically as well. Most DMs I've played with apply it only when the action has been used to see and hear through the familiar, but a fe have gone with the broader limitation.
...
Beyond all of this, there are dozens of other abilities (dominate monster/person, monster abilities, helm of telepathy, etc...) that all have their own rules. You have to read the individual rules for the telepathy to which you have access, and let the DM fill in any gaps.
Great Old One Warlock, Awakened Mind:
You can telepathically speak to any creature you can see within 30 feet of you. You don’t need to share a language with the creature for it to understand your telepathic utterances, but the creature must be able to understand at least one language.
This one allows you to speak to, but not receive messages from, a target creature within 30 feet (confirmed in Sage Advice). As long as it understands a language, it can understand you, and anything you can do in speech you can do in this telepathic one way conversation (yell, whisper, modulate your mental voice, etc...). There is nothing to indicate that the target will know the source of the speech if you do not identify yourself, so whether they do or not is up to the DM (unless you identify yourself in the communication). You must be able to see the creature to use the ability.
I had a Circle of the Moon Druid PC in a game that took one level of Great Old One Warlock (making a Pact with an alien nature spirit). Hex (which it could redirect while wildshaped), Armor of Agathys (not concentration and is nasty with high level druid spell slots) and Awakened Mind were iconic elements of his combat identity - a very efficient, evocative and creepy PC.
Telepathy (MM monster ability)
Telepathy is a magical ability that allows a monster to communicate mentally with another creature within a specified range. The contacted creature doesn’t need to share a language with the monster to communicate in this way with it, but it must be able to understand at least one language. A creature without telepathy can receive and respond to telepathic messages but can’t initiate or terminate a telepathic conversation.A telepathic monster doesn’t need to see a contacted creature and can end the telepathic contact at any time. The contact is broken as soon as the two creatures are no longer within range of each other or if the telepathic monster contacts a different creature within range. A telepathic monster can initiate or terminate a telepathic conversation without using an action, but while the monster is incapacitated, it can’t initiate telepathic contact, and any current contact is terminated.
A creature within the area of an antimagic field or in any other location where magic doesn’t function can’t send or receive telepathic messages.
You do not need to see the target (although they must stay in range), it is two way communication, and once initiated it can continue so long as they stay in range (as specified in the ability). This ne is not labeled as "you speak", so a DM might rule that changes of inflection and volume are not possible here - that the telepathy here is not capable of the modulations we have in speech.
Telepathic Bond Spell
You forge a telepathic link among up to eight willing creatures of your choice within range, psychically linking each creature to all the others for the duration. Creatures with Intelligence scores of 2 or less aren’t affected by this spell.
Until the spell ends, the targets can communicate telepathically through the bond whether or not they have a common language. The communication is possible over any distance, though it can’t extend to other planes of existence.
This is a far reaching communication that is not limited by range, but as it lacks that "speak" language, the DM may say that inflection and volume changes are not possible. This does not require a common language, or any language at all (so long as they have intelligence 2), so it is quite more versatile than the previously discussed forms. It is also not necessarily clear who the speaker is amongst those involved in the circle. All of that is up to the DM. Minimum Intelligence 2.
Early in 5E I played a Great Old One Warlock. He was pact of the Tome, and he used this spell with the party all the time despite having the Awakened Mind ability. They each had advantages that the other lacked.
Telepathy Spell
You create a telepathic link between yourself and a willing creature with which you are familiar. The creature can be anywhere on the same plane of existence as you. The spell ends if you or the target are no longer on the same plane.
Until the spell ends, you and the target can instantaneously share words, images, sounds, and other sensory messages with one another through the link, and the target recognizes you as the creature it is communicating with. The spell enables a creature with an Intelligence score of at least 1 to understand the meaning of your words and take in the scope of any sensory messages you send to it.
Longer duration, allows communication with a creature of intelligence 1, and you can transmit more than words.
Telepathic (Feat - UA)
You can speak telepathically to any creature you can see within 30 feet of you. Your telepathic utterances are in a language you know, and the creature understands you only if it knows that language. Your communication doesn’t give the creature the ability to respond to you telepathically.
Very similar to Awakend Mind, you get to speak and it is one way communication.
Enhanced Find Familiar Telepathic Bond
The [familiar] can serve another creature as a familiar, forming a magic, telepathic bond with that willing companion. While the two are bonded, the companion can sense what the pseudodragon senses as long as they are within 1 mile of each other. While the [familiar] is within 10 feet of its companion, the companion shares the pseudodragon’s Magic Resistance trait. At any time and for any reason, the [familiar] can end its service as a familiar, ending the telepathic bond.
There are no words exchanged, just senses, with an enhanced familiar.
Find Familiar
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has. During this time, you are deaf and blind with regard to your own senses.
This one is ambiguous in a key regard - the "During this time" statement could apply to only when you see and hear through the familiar, or any time you communicate with the familiar telepathically as well. Most DMs I've played with apply it only when the action has been used to see and hear through the familiar, but a fe have gone with the broader limitation.
...
Beyond all of this, there are dozens of other abilities (dominate monster/person, monster abilities, helm of telepathy, etc...) that all have their own rules. You have to read the individual rules for the telepathy to which you have access, and let the DM fill in any gaps.