Basically Ocarina of Time on N64 screwed things up by having Link violate the Temporal Prime Directive at the end of the game, creating a split timeline. This new game handles it by pretty much flatly refusing to place itself in any of the potential post-OoT timelines, and by also setting itself at least 10,000 years after any previous game.

Link-wise, most Links are supposed to be reincarnations of the same guy, but that's never really explored as a plot point. Zelda is arguably a more important and better explored character than Link in Breath of the Wild, too, but you need to find a lot of memories around the world to discover this.