While Abrams is allergic to talking about his movies before release date, Benedict Cumberbatch, who plays John Harrison, the movie's bad guy, has denied that this film is in any way related to "Wrath of Khan". For one thing, it wouldn't even make any sense - nobody's found the Botany Bay and likely never will (since it's one tiny ship somewhere in a sphere about 200 lightyears across, centered on Earth - makes a needle in a haystack seem like something really obvious). For another, for this to be a remake of TWoK, there would have to have been a "Space Seed" to lay the groundwork, and there wasn't.
I'm wagering that this is an exploration of what would have happened if another ship than Kirk's Enterprise had hit the galactic barrier - the one that gave Gary Mitchell godlike psychic powers in "Where No Man". Only this time, the ship's captain didn't have a Spock there to tell him to kill Harrison before it was too late...
_________________
Sodium is a metal that reacts explosively when exposed to water. Chlorine is a gas that'll kill you dead in moments. Together they make my fries taste good.