got three hours of sleep so sorry for any spelling or grammar errors. all that follows is just my own headcanon.
prime - it's unclear what category she'd be under, mostly because no one is sure how much power she holds.
omnipotents/cores - major gods, usually at the head of a pantheon. this would be entities such as dreamxd. usually just referred to as higher deities. in spite of their title of omnipotent, they do have minor limits and can be subdued, though it's an incredibly difficult task to do so.
secondary cores - similar to omnipotents in terms of power, but serve under a core and are forced to obey them, limiting their power. this would be where mumza falls.
outer cores - secondary cores without the connection to an omnipotent. technically speaking, this would be where both herobrine (you forgot he was canon, didn't you?) and the egg go.
minor gods - don't have the access to the heavens other gods have, nor are they as strong. powers here would mostly be in terms of insane physical ability and vague mystic/otherworldly connections. most important note here is that their titles and immortality are transferable. for an example, technoblade became the blood god after killing the previous holder of said title, becoming the blood god himself and gaining those powers.
immortals - similar to minor gods, but were born naturally with eternal life. titles are not transferable. this would be eret's position, along with those like her.
the chosen few - also known as angels, these are mortals that have been chosen by gods to become immortal, usually being blessed in some specific way (think phil's wings). in addition to phil, foolish would technically be under this banner, though he's of a far higher ranking than any other chosen. if we squint, fundy might be a lesser chosen, which i may or may not elaborate on. we'll see. immortals and a few minor deities can qualify for this ranking.
*NOTE: though these are all individual and nuanced terms, no one really uses them on the dsmp. if you're an immortal, you're a god. if you're a core, you're a god. rarely would you see someone refer to xd as an omnipotent, or foolish as a chosen.
might make a p2 one day but that's it for now o/