What is the difference between a forward slip and a side slip? 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?
There is no difference aerodynamically. The only difference is in intention and presence of the wind. The airplane does not care about the ground track, all it feels is the movement through the air. Both side- and forward-slip make the airplane fly slightly sideways through the air, somewhere in the direction between nose and downwards pointing wing.

If there is no wind, your ground track will be exactly the same, between wing and nose, and you will feel that the nose points away from your track and call it forward-slip. If the wind is blowing and you manage the right amount of slip, you are moving sideways through the air, but the ground track (combination of wind- and slip- movement) can be aligned exactly with the nose and you call it side-slip.

There is really no difference aerodynamically and thus no difference in applied controls either.