as someone who used to rp in the genre, the simplest answer is "basically a panfandom, but instead of playing actual canon diluc having been brought from actual canon genshin impact with all of the actual canon events, you're instead playing modern au diluc with an adaptation of that canon backstory (like having his dad die while investigating police corruption + kaeya outing himself afterwards as being involved with organized crime + diluc quitting his old job as a cop to instead become a vigilante) and everyone goes from there."

the more in-depth answer is that they're actually supposed to be two entirely different concepts - if i remember correctly, the personified sites are supposed to be that description up there with the "make an au version of the character in this setting" concept while spirits sites are supposed to be a bit more like once upon a time where the characters are drawn from their original worlds somehow + just have their memories messed with so they think they belong here. or, as a different example, i think that zugzwang's "give up your memories" concept would get you pretty close to how the spirits concept is supposed to play out. but i also know the two terms are used p interchangeably within the community itself (these days anyway), so you'd have to look at the individual site to see how they're rolling with it.

like i said, it's actually a super fun + creative concept, i loved when i was in the personified side of it because it was always so fascinating to see how people would adapt their characters into the modern day + no two people adapted the same character the exact same way, and it was also super cool to see some of these absolutely wild new crossover connections people would throw in (like i remember someone had that maximus from tangled was the younger brother of frollo's horse from hunchback) since it opened up entirely new plotting avenues to explore + made it a lot harder for people to bubble. also it was wild some of the ships people would come up with pour one out for that scar x shere khan crackship i regularly stalked the threads of and it was just. such a good time.