Other than a couple of graphical changes (ie. a bus instead of a plane and using an umbrella instead of a parachute when jumping out), it's practically the same. The only difference I saw was that as Fortnite has a building mechanic, that has become part of Battle Royale as well.
As for Battlegrounds, it looks good and am hoping that it comes to PS4 one day (Microsoft bought the exclusive rights to it, though unsure for how long).