i was asked about demon subtypes lots of times, now i tried to compile something with no claim to completeness or accuracy.
you cannot put a demon into exactly one category. there are lots of "subtypes" you could define, and even then half the demons would say they're not part of (exactly) one of these. moreover, types can change during a demon's lifetime.
but i have seen this question a couple of times recently, so i'll try to give you some general categories to work with:
* companion/guardian/familiar: a demon who accompanies another being, working as their guard, friend, and/or helper. (the term "familiar" is used for the helpers/companions of witches/sorcerers/whateveryoumaycallthem.)
* devil: often used for brutal demons (but also other creatures) that take pleasure in making others suffer.
* dreamwalkers: enter the dreams of human beings. succubi/incubi are subtypes of this category.
* fallen angel: some people say that fallen angels can become vampires under certain circumstances. i think it's up to the angel to define themself as demon or not.
* fear-eater: specialized in ingesting emotional energy, more exactly fear, they will do anything to scare you. i've written an article about them.
* shadow/shade: don't mix them up with the kin type "shadow". these creatures rarely interact with humans and are often seen as a shade in the corner of your eye.
* shapeshifter: most demons have an ability to change their form, behavior, and energy pattern. shapeshifters are very talented in doing so.
* succubus/incubus: a demon who lives off sexual energy. succubi are "female" (seducing men), while incubi are the opposite.
* trickster: a demon who enjoys (or draws energy from) tricking others - mostly without bad intention, but it's not unheard of that they caused harm to their targets.
* tutor: a demon who teaches you things. be careful there, as always you could fall prey to an imposter.
* vampiric demon: a demon who needs to ingest the energy of other beings. often specialized in one type (see fear-eaters).
* watcher/observer: a very curious demon watching humans (and other beings) and trying to understand them.
as i said, these categories practically don't exist. no demon is exactly one of these, most combine several traits, and there are surely some who don't fit into any of these "subtypes". it's just for those who like to work with labels.