Yes, the Bass Whammy has different intervals than the Whammy IV. It is not just different intervals though, it is also different treadle behavior. If you look at this list you can see that the heel/toe treadle positions are quite a bit different from the Whammy IV or the V, the Bass Whammy is specifically tailored for bass.
Bass Whammy
Harmony:
Oct Up/2 Oct Up
Oct Up/10th Up
Oct Down/Oct Up
Oct Down/4th Oct Down
5th Oct Up/6th Oct Up
5th Oct Down/5th Oct Up
5th Oct Down/4th Oct Up
4th Oct Down/3rd Oct Up
Whammy:
2 Oct Up
Oct Up
5th Up
4th Up
2nd Up
2nd Down
4th Down
5th Down
Oct Down
Dive Bomb
Shallow Detune
Deep Detune
Whammy IV
Harmony:
2nd Up/3rd Up
Min 3rd Up/3rd Up
3rd Up/4th Up
4th Up/5th Up
5th Up/6th Up
4th Up/7th Up
4th Dn/3rd Dn
5th Dn/4th Dn
Oct Up/Oct Dn
Whammy:
2 Oct Up
1 Oct Up
1 Oct Dn
2 Oct Dn
Dive Bomb
Drop Tune
Shallow Detune
Deep Detune