In NAIR 4.0.0, NAIR players can go online, get in a lobby hosted by a DAIR player, and play DAIR. (And of course, vice versa.) You don't need to own DAIR to play DAIR if you have NAIR. Sorry, I know that's a mouthful.
The cross-game multiplayer compatability is the only added added feature of 4.0.0
DAIR is a new game (available on Steam) featuring a different move, a different stage, and different rules. DAIR releases August 1st.