To a degree, they're covered by both. I now have to say that I am not a lawyer, although I have been a legal researcher, and my expertise comes from experience in publishing and should not be considered legal advice. So, Steamboat Willie and the Mickey Mouse who appears is covered by copyright. However, Mickey Mouse, the character used for commerce and as a mascot by Disney, is covered by trademark. This means that in a few years, the version of the character who appeared in Steamboat Willie will be in the public domain, but the Disney mascot will covered under trademark.
The question is whether it is transformative. If I was to start with somebody's character (such as Altair from Re:Creators) and use them as a writing prompt, creating a new character with a similar yet modified back story but different personality (now named Aquila) this is transformative and thus a derivative work. Aquila has the DNA of Altair inside her, but she is a new character with her own personality and character arc.
(And yes, this is a real example, and everybody gets to meet her in mid-December.)
To bring that to AI art with copying and pasting, if you just take a person from one picture and put them on a new background, then it probably isn't transformative enough to count as a derivative work - it's still that same person. If you take this person, replace their head with a toaster, and call them "Toaster Head the Great," this would be transformative, and thus a derivative work. It is no longer the same person, and all of the elements (body, toaster, background) have been used to create something new.
EDIT: Hopefully that makes sense.