okay I haven't spelled this out directly mostly because I forget not everyone already knows all this stuff so here's, I think, the funniest detail of the "is Pauline really the Lady from Donkey Kong" "controversy".
the game that introduced Pauline's modern design (and the first time she was given that name in Japan) was Donkey Kong (1994), a reimagining of the original arcade game released the same year as Rareware's Donkey Kong reboot.
Donkey Kong (1994) also happens to have Donkey Kong Jr. in it, who is visibly younger than Donkey Kong. this suggests that the "Donkey Kong" that appears in DK94 is not "Donkey Kong III" from the DKC series, but really is the same Donkey Kong from the original arcade game.
what all of this means is.
if you decide to interpret "Pauline" and "Lady" as different characters, this still wouldn't make the timeline make sense! because even if "Pauline" wasn't really there in the original arcade game, she still was kidnapped by the original Donkey Kong at a point in time before Donkey Kong III would have been born, an event that happened in the first game that contains "Pauline" as opposed to "Lady"!
and isn't that so good? like, there's literally no way to make the timeline make sense without time travel or arbitrarily cherry-picking which Nintendo-developed games count as "canon"! no matter how you slice it, Pauline has to simultaneously be 13 years old when Donkey Kong III is a grown adult and a grown adult before Donkey Kong III was born. beautiful