The difference is this.

BOTW =

Zelda creator last real game before he kick the bucket.
Has the flower lady/girl who gets upset and TKO Link ( like the GB game if you steal ), or Cukkoo's.
Actually had a western programmer on board ( the animal critters ). Who was a Zelda fan as a kid.
You could literally beat the game early from the start and fight this unfinished version of, getting ending 01 out of the way.

TOTK =

Attempts to tie in all of Nintendo's spoofs
Make the Story about Aliens / Visitors of another world.
The Flower lady no longer K.O. you and there is no animation or anything at all.
The Dragon from Dragon Ball fights with another Dragon like itself and you do some sorta thing.

If you have BOTW, I would probably keep it sealed and just find other means of playing the game.
Otherwise finish BOTW first then dig into TOTK. Your not really missing anything. Same Hyrule only more Sky areas and messed up lore.