I am having a hard time understanding what differentiates the two types of slip. I understand that in a forward slip, the longitudinal axis is tilted with respect to the flight path, whereas in a side slip it is not. In a forward slip your track stays the same, whereas in a side slip it would (in the absence of wind) cause you to track toward the down wing.
My difficulty comes from the fact that the control inputs needed to enter both are the same: banking with opposite rudder.
Why then is the heading of the aircraft with respect to the flight path different, if the control inputs are the same? Is it just a question of degree, which is to say, the forward slip just requires more rudder?