It seems that:


Burtonverse

Batmobile
Batwing
Batmissile (Batmobile's alt.mode in "Batman Returns")
Batboat - hopefully! Sorry, I can't truly stand the name "Batskiboat" that many reported, it seems too long.


Nolanverse

The Tumbler - I just don't think this iteration was ever named "Batmobile" on-screen.
Batpod
The Bat


Am I right?