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 (2022 MCU TV series) S01E05 "Asylum", where it was mentioned by Taweret, an Egyptian goddess*, that there are "many intersectional planes of untethered consciousness" and that the Ancestral Plane is one of them.
* Bast in Black Panther is also an Egyptian goddess.
Dialogue from Moon Knight S01E05 "Asylum" (emphasis mine):
Taweret: You'd be surprised how many intersectional planes of untethered consciousness exist. [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. Taweret was explaining to them what the Duat is. 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.
In Black Panther: Wakanda Forever, Shuri's vision of the Ancestral Plane is also different from T'Challa's. Her vision was of the flooded Wakanda throne room (reflecting recent events she experienced) and the person she met was not her father, brother, mother, nor any ancestor, but Killmonger, reflecting her state of mind at the time.