I'm not sure if it is better to "give the possible dups an answer this question covers and they only touch" or to stick here. So I stick here.
Stellen, Abstellen and Aufstellen have something in common due to "stellen" - and yet they are quite different. They might replace each other - but only figurativly.
The difference comes with every prefix and suffix and with the addition of something / someone / somewhere / direction / time / relation / literal / figurativly ... well, with all aspects a sentence can offer.
I try to transform the different translations to show their figurativly connection. DWDS provides various examples. I picked some with lesser surrounding words to point out the vast variety of meaning while similarity exists.
- put sth on a specific place and have it somehow "upright"
- to catch so. (could be transformed into "you put yourself next to him/her")
- to force so. to stop (like catch so. just not being already next to him/her)
- to put so. into trial (could be transformed into "announce that so. has to be put in front of a court)
- turn something off
- put sth somewhere so it is not carried any longer (could be transformed into "turn a carriage duty off")
- to decide that so. has to do a different task (could be transformed into "turn current duty off to be free for another already named duty")
- remove / stop a problem (could be transformed into "you turn the problem's existence off")
- to relate a theory an a different base, like in law where you "darauf abstellen, dass ein Sachmangel vorlag" [take into account that there was already a deficiency] (could be turned into "you turn further arguments about this topic off due to already having an explained base)
- to erect sth somewhere: a sign on a field, a
- to be announced as a candidate/ position, e.g for an election (could be transformed to "erect a list with names on it")
- you could "ein Verbot aufstellen" (could be transformed into "erect a prohibition")
- you could "create a theory" (could be transformed like the prohibition: in the world of theories, each stands its own ground and can be erased by arguments)
- you could "create a formation" - that is close to "stellen" since you decide to put sth./ so. on a place while it is not necessary that it is fulfilled immediatly (what "stellen" would)