I agree with BotD. Wikipedia is good, but it's not the be all and end all of Buffyverse facts. Especially not in cases like this, where there is no consensus amongst fans as to whom classifies as what. On Wikipedia they all (plus the First Evil) fall under the category of Fictional Deities, because that makes them easier to understand for laymen. The problem in this debate is that we have haven't really got to much hard facts to base our theories on.
---- Onto the actual discussion on gods. ----
I think that in this context the term god has two distinct uses. First, it is a label or title people both inside and out the fictional universe use to denote those of great power. Secondly, in more absolute terms god might refer to an actual species, like human, dog, or vampire. So what is it? God as species or god as title?
God as Species
If you consider a god to be a species, you might be prone to think that since Jasmine, Illyria, and Glory displayed such vastly different powers and abilities, that only one of them is truly a god. Therefore, I think it would not be exactly correct to say that a god is a type of species, but rather it might be a family of species or an order or a class. Perhaps it is even an entirely different kingdom, ie in addition to animals, plants, fungi, and bacteria, there might be a fifth category for gods. In fact, I would argue that demons would be counted as another additional kingdom. (Check out some articles on wikipedia on Biological Taxonomy.)
Anyway, if you were to treat god as a different kingdom, it might be easy to see how Illyria, Glory, and Jasmine all fall under the same banner, because they might be completely different species all, in completely different families and classes. Just think of how different insects, frogs, and humans can be; they too are all different species in the same kingdom. If you regard god as a species or group of species, some unclassified Supernatural entities from the Buffyverse might also fall in this category such as the First Evil and the Ra-Tet, but Willow certainly wouldn't.
God as Title
It is equally possible to imagine that the term god has nothing to do with the biological classification of beings in the Buffyverse, but that it is instead merely an honourary title bestowed upon those with great power. Just a couple of ranks up from Governor, King, Emperor is the rank of god. Some real-world rulers have even been called gods-incarnate or have called themselves it. The way Illyria describes herself as "god-king of the primordium" it certainly sounds like a title. Question is of course, what what do you need to qualify for this title? Vast powers is a probably a good start, although this is very relative and subjective. In the world with nothing but shrimp, a lobster might already be considered a god. The key ingredient would seem to be worshippers. Is as many as one enough to be considered a god? Or do you have to be revered by a substantial amount of people/entities? Probably, but again, that's pretty subjective. Also, what if you don't consider yourself a god, but are worshipped as one: does that make you a god? Whatever your subjective standards are, if you look at the term god this way, Jasmine and Glory are without a doubt gods. Illyria, however, could be called a former-god, because she only had one known worshipper left, and he's pretty dead. If you look at it this way, Kennedy may have been right in calling Willow a god, if she herself worshipped her like one. But the Ra-Tet are not gods by this definition.
Solution: God as a little bit of both??
I think that perhaps in the Buffyverse a god is neither of the above exactly, but more like a little bit of both. I do think that there might a separate species or group of species for extremely powerful, immortal entities, which (by human standards) have all the qualities of gods. But the entities in this group are probably not entirely congruent with the entities that are venerated as gods in the entire Buffyverse. For example, in the world with nothing but shrimp, the lobster, an entity which is clearly not of the god-species, could still be worshipped. On the other hand, in a world where only god-species entities live, they might not recognise each other as gods, because they are all on the same level.
So, that's how I look at it. Glory is a Deus Infernus, Illyria is an Unus Anticus, and Jasmine is a Potensus Est; three different distantly related very powerful species in the biological kingdom of deii. In addition, all three of them were/are/have been worshipped as gods.
