With a non-exclusive tag, players are given the ability to negotiate with other teams. The original team can match any offer, but if they don't and the player signs to another team - the original team is entitled to 2 first round picks as compensation from the new team the player signed with.
Miami's going a different route with their tag;
Seems like a lose-lose situation here. Also can't remember the last time i seen a transition tag used over a franchise one.
Edit: Apparently Miami did the exact same thing with Clay last year. lol.