"Cutting in" means that you manage to enter the lane of your choice, while "cutting off" refers to getting in the way of another driver (or at least, the other driver perceives it as such). They may both refer to the same maneuver, but there's a difference in point of view / interpretation.

Cut in is you doing it. Cut off is the action. Example you can "cut in front" of some one, and by doing that you "cut them off"

Cutting in can be done in a way that is friendly between the people involved but cutting off is usually not done in a friendly manner.