Celebrim
Legend
I've always split the deities into a number of categories. The two big questions are "Is there such a thing as actual divinity in the game world?", and "How much does worship empower a being in the game world?"
Those two questions are actually not at all straight-forward in my cosmology.
To the first, you have to define what you mean by "actual divinity" and that turns out to not be a straight-forward thing to do. In terms of being an uncreated being, the only possible deity in the setting by that unknown creator who doesn't appear in the setting and who was gone from the setting before the gods were even around. There are All Father and All Mother cults that worship that being but they notably have no clerics. It can be presumed that either that creator doesn't hear or doesn't care to intervene.
If by deity you mean, "worthy of worship" then that is still a burry line. If you worship the gods, can you not also worship the fey and animal spirits who preexist them? Can you or ought you to worship the giants and dragons, who are decedents of gods? This is major topic of controversy within the game world, but the while the major cults try to suppress general worship of everything (for reasons both bad and good depending on how you look at it) the bulk of the public makes no particular distinction between offering up prayers and sacrifices to ancestors, animal spirits, local fey, and the gods. For that matter, how is that different from making requests to your king and paying him taxes and tribute?
Of course, in the setting a lot of people answer, "Deity means the beings who were born directly from the fruit of the Tree of Life" to which some would add, "...as well as perhaps their most immediate heirs and offspring that are fully of that divine nature and not mixed with anything else." and as a practical matter for a good portion of the campaign world, "This socially and legally approved list of deities that I'm allowed to worship or proselytize on behalf of without getting burned alive by my neighbors and/or the authorities."
For the first question, consider - is there a distinction between an archdevil/archdemon and a deity from the same plane?
This one I can definitively answer, "Yes." Order of being in my game is strictly defined by mode of creation. I generally don't use archfiends of any sort because this D&D contradiction was one of the areas I was trying to clean up and because I have a thousand different gods and can invent one on the spot to do that job, but when I do feature them they're essentially seneschals or ministers of the evil deities - greater servitors vested with divine authority and created to fulfill purposes by those deities either directly created by those deities or forged from some spontaneously existing spirit of evil (since spirits tend to spontaneously generate in my setting whenever you have a lot of something). An archfiend is fundamentally no different in order of being than a Solar or Planetar, but of a very different order of being than a god. Celestials and fiends and the great majority of outsiders are Greater Servitors - direct creations of some deity. That said, the Modron and Slaad are weird and don't seem to follow that general rule. Primus is comparable to a god or is perhaps some sort of strange lawful aligned fairy lord, and the Slaad Lords are no one's servitors. Technically Modron and Slaad might have orders being different from everything else in the setting, and LN and CN deities have their own separate Greater Servitors that are neither of those things (Inevitables, perhaps?).
Another reason to not worry too much about archfiends in my game is that since they aren't particularly special, there are literally dozens of other things that have more or less equal rank and power. For example, remembering that giants are offspring of the gods, something like the king of the Fomorians is of at least equal and probably greater rank (a demigod) to an archfiend. The aforementioned Prince of Cats ranks with any archfiend, as would someone like Mother of Apples. Heck, the nymph of one of the world's largest rivers probably ranks with an archfiend. Fey monarchs like Oberon and Titania and Mag just out rank any archfiend (and probably rank with gods), as does someone like Alcegraf Lord of Griffins or the Sultan of the Efreet or the Caliph of the Djinn.
And again, all this mess means answering "What is a divinity?" is just a mess. Pick your definition of divinity and apply it is the best people in the setting can do. Is that pond nixie a divinity? Sure; why not?
Is it merely a difference in power? Or is it intrinsic in nature? Can a archdevil be more powerful than a deity?
a) There is a difference in power but it's not merely a difference in power.
b) Yes.
c) No, though I suppose that depends on how you define "power". A greater servitor of a war deity might potentially represent a nigh unbeatable challenge to a lesser deity that wasn't potent in the sphere of martial combat but in terms of authority it wouldn't be much of a contest. A very weak deity would be able to exercise much greater authority over their domain than even the most powerful greater servitor could over anything. And certainly, the combat ability of even the least martial god would be closer to that of even the most potent greater servitor, than would be the authority of the servitor to the authority of the god.
A greater servitor can give a person a spell, but they would in doing so usually give up the ability to use that spell themselves (especially if the spell is a non-trivial sort) and generally must devote a non-trivial amount of attention to the act of transferring the spell to someone. A god can't support a limitless number of clerics, but for the most part granting a spell by a god gives up no power and requires a trivial amount of attention. Most gods could simultaneously delegate spells to hundreds or thousands of worshippers at a time while still having enough spare moments to miraculously intervene hundreds of times in the world and pursue their own interests. A greater servitor probably could only manage a handful and would be distracted from everything else while doing it. It's sort of like asking for the answer to the question, "Which has more heat, a furnace heated to three thousand degrees or a moon heated to only a hundred degrees?" The furnace seems a lot hotter and might seem locally more potent, but if you could extract all that heat to do work the difference turns out to be immense.
As for what anyone gets out of worship, the official answer is nothing. Like many of the official answers, that answer is wrong or a lie. While not every deity is aware of it, as a campaign level secret, they are actually reaping benefits from worship. It isn't the source of their power, but it does enlarge their power. Certain things that deities can do "at cost" that aren't repeatable like create artifacts, dominions, sacred sites, or new greater servants or other epic scale works of divine might become repeatable. The deities aware that this is happening are absolutely terrified by it and do not talk about it with mortals or even their own servants. This is part of the big terrifying thing that "went wrong". The deities that are aware of it happening couldn't answer the question of whether their seneschal getting worshiped would garner the same benefit, but you can see why this is one of the reasons the deities aren't exactly promoting the worship of anyone but themselves or allied deities. If the PC Shaman's in my game actually knew that this was true, it would raise another level of questions regarding the social/cultural/supernatural conflict between Shamans and Clerics in my game world. If the shamans or their patrons actually figured this out, they'd almost certainly create a heretical branch that believed the gods discouraged shamanism because they were afraid of Shamans creating new gods. And almost immediately, society would go into conflict over whether being able to create new gods was a good thing or a bad thing, as well as cause certain heretical groups to be reevaluated for good or ill. For example, the Kelterists are the most prominent group that believe the gods are powered by worship, but they are focused on the idea that gods are created by worship and want to uncreate them by stopping their worship.