I'm pretty sure Goku is the one who kills Frieza in the Cell Timeline. Cell (Post Jinger) only knows that the Androids of his Line are stronger than his current I, not necessarily as strong as the Androids of the Main Line.
If a Future Trunks had killed Frieza in the Cell Line, then he would have given the medicine to Goku and everyone would have trained just like in the Main Line. If that had been the case, Cell when he saw Vegeta for the first time on the Main Timeline, he would not have said "Vegeta is still alive, he has also become very strong". Therefore, Vegeta of the Cell Line is not as powerful as the Vegeta of the Main Line.
When Cell reveals his identity to Piccolo in the Manga, they only show images of the death of Frieza and King Cold, it was more like a copy and paste the images when they had been killed by Future Trunks. Then Cell says he could get Cells from a Warrior named Trunks, but that does not mean he necessarily referred to the same time that Freezer and King Cold had been killed.
In the Anime, it must have been a mistake to show Future Trunks killing Frieza and King Cold in the Cell Timeline. It must have been again a copy and paste that scene. It was a possible plot error.
I think the Future Trunks and Cell lines were identical, but with the difference is that in the Future Trunks Line, this was strengthened in the past and could kill Cell, while in the other Line did not happen the same.