If I was to try and codify all the magic systems in standard D&D and change up the mechanical expressions to give us different "types" of magic systems... I might do something like this:
Planar magic (also called "Divine" by some people) would be magic granted to worshippers on the Prime plane from beings from the planes and use pact magic casting. So Warlocks and Clerics (and Paladins) have small amounts of spells, but always cast at the highest level. They also have Invocations (or Miracles or Oaths) that grant them magical ability that does not require spells or spellcasting. In order to gain access, you have to pledge yourself to an extraplanar being and they may choose to bless you with power.
Primal magic (magic that comes from the Prime plane) would be considered something like "the Force"... the energy of the planet a person is on that certain people are able draw from in varying quantities. This would be your Druids and Sorcerers (and Monks) and would be all Spell Point based. These magic users do not have a set formula of "you can this amount of spells at this level, that number of spells at that level" that spell slot casters go... but rather they draw from a pool of energy in whatever quantities they want (hence the spell points) that comes out of them, whether by spells or by wildshaping/bodyshaping. (And personally I kind of like the idea that certain Sorcerers/Monks could have their own versions of "wildshaping" based upon their magical origins... a draconic sorcerer can begin to bodyshape and take on aspects of a dragon, a monk could bodyshape and begin to transform their body into something as hard as diamond, etc.)
Finally there is Arcane magic, (or technical magic) that comes from the astral and ethereal planes. This "Weave" of magical energy is connected tenuously to the Prime plane and if you study and work and learn the techniques necessary to tap into it in very specific ways, you can generate magical effects. So this would be your Wizards, your Bards, your Artificers all of which use Spell Slots. These classes are all about the "scientific blueprints" you need to create spells-- either the magical incantations of a Wizard that are written down in a spellbook, the magical aural and somatic notes you need to experiment with and then play as a Bard, the actual blueprints you create as an Artificer. And this is why everything is so regimented in the Spell Slot system... there's a science to it that has to be followed in order to be able to tap into that arcane font of magic.
What's important to note is that unlike the other two types, anyone can become an Arcane magician, so long as they study it and work hard at it. Planar (or Divine) magicians have to be granted their magic through their pacts and/or worship, and Primal magicians have to be born with it. Arcane spellcasting is open to everyone else and is the egalitarian magic.
Planar magic (also called "Divine" by some people) would be magic granted to worshippers on the Prime plane from beings from the planes and use pact magic casting. So Warlocks and Clerics (and Paladins) have small amounts of spells, but always cast at the highest level. They also have Invocations (or Miracles or Oaths) that grant them magical ability that does not require spells or spellcasting. In order to gain access, you have to pledge yourself to an extraplanar being and they may choose to bless you with power.
Primal magic (magic that comes from the Prime plane) would be considered something like "the Force"... the energy of the planet a person is on that certain people are able draw from in varying quantities. This would be your Druids and Sorcerers (and Monks) and would be all Spell Point based. These magic users do not have a set formula of "you can this amount of spells at this level, that number of spells at that level" that spell slot casters go... but rather they draw from a pool of energy in whatever quantities they want (hence the spell points) that comes out of them, whether by spells or by wildshaping/bodyshaping. (And personally I kind of like the idea that certain Sorcerers/Monks could have their own versions of "wildshaping" based upon their magical origins... a draconic sorcerer can begin to bodyshape and take on aspects of a dragon, a monk could bodyshape and begin to transform their body into something as hard as diamond, etc.)
Finally there is Arcane magic, (or technical magic) that comes from the astral and ethereal planes. This "Weave" of magical energy is connected tenuously to the Prime plane and if you study and work and learn the techniques necessary to tap into it in very specific ways, you can generate magical effects. So this would be your Wizards, your Bards, your Artificers all of which use Spell Slots. These classes are all about the "scientific blueprints" you need to create spells-- either the magical incantations of a Wizard that are written down in a spellbook, the magical aural and somatic notes you need to experiment with and then play as a Bard, the actual blueprints you create as an Artificer. And this is why everything is so regimented in the Spell Slot system... there's a science to it that has to be followed in order to be able to tap into that arcane font of magic.
What's important to note is that unlike the other two types, anyone can become an Arcane magician, so long as they study it and work hard at it. Planar (or Divine) magicians have to be granted their magic through their pacts and/or worship, and Primal magicians have to be born with it. Arcane spellcasting is open to everyone else and is the egalitarian magic.