Hi! Pokémon Origins is a separate miniseries, following the Kanto game's storyline more closely than the original anime (with Ash) does. It follows trainer Red and his Charmander, and also featured some surprise Mega Evolution. I reeeeally liked the animation style of Origins! So very much better and more vivid than the imo a bit static usual pokémon anime animation.
Generations I don't know much about yet, sorry. Perhaps somebody else can answer that!
Edit: this seems to be helpful
https://www.pokecommunity.com/showthread.php?t=378077