This cannot be more simple:

Arcade: Cranky Kong and Lady
DKC: Cranky Kong's son, Donkey Kong. "Donkey Kong" itself is a title passed down from Cranky to Donkey.
Bananza: Donkey Kong Jr has grown up and now inherits the title of 'Donkey Kong'. It explains why he was in the spinoff games, why Mario Kart World uses Jr as a stand-in for Donkey Kong, and why DK doesn't chimp out (heh) when he sees K.Rool.