I've always thought of it like a plane, with the terms adverse yaw and adverse roll applying. The main difference is if your turn is uncoordinated, you fall over. Yaw is controlled via the handlebars. Roll is controlled via balance.

Just turning the handlebars causes adverse roll in the other direction. If you are falling to the left, turning the wheel to the right causes an opposite roll and restores balance.

Turning the handlebars the opposite way momentarily is a great way to start a turn because of the adverse roll that it causes.