Killmonger's Ancestral Plane vision is different because each person perceives the "planes of untethered consciousness" differently.
The Ancestral Plane is expounded upon in Moon Knight S01E05 "Asylum", where it was mentioned by the Egyptian goddess and Ennead*, Taweret, that there are "many intersectional planes of untethered consciousness" and that the Ancestral Plane is one of them.
* Note: Black Panther's Bast is also an Egyptian goddess and an Ennead.
Dialogue from Moon Knight S01E05 "Asylum" (emphasis mine):
Taweret: You'd be surprised how many intersectional planes of untethered consciousness exist.
Taweret: (GASPS) Like the Ancestral Plane. Oh! Just gorgeous. Anyway.
The background to the scene where the above dialogue took place was that Marc Spector (Moon Knight) and Steven Grant (Marc Spector's alter-ego) were in a realm called the Duat. In Moon Knight, the "planes of untethered consciousness" are called the Duat, and in Black Panther, the Ancestral Plane.
Taweret: Because the Duat's true nature is impossible for the human mind to comprehend, you may perceive this realm as something more easily recognizable to you.
Killmonger's Ancestral Plane vision is different because each person perceives the "planes of untethered consciousness" differently. Unlike T'Challa, Killmonger didn't grow up in Wakanda, so he isn't as familiar with Wakandan traditions and views as someone like T'Challa, who grew up in Wakanda and was groomed to be the next king and Black Panther.
Killmonger's vision of the Ancestral Plane is something more recognizable to him, based on his past, in the apartment he grew up in and with his father, and not including his other ancestors or past Black Panthers who he won't be as familiar with.