Personally I find these attempts to differentiate between "forward" and "side" slips erroneous and unhelpful.
Generally, I agree. In the case of both maneuvers, what the airplane experiences would be identical. The
only difference (presuming the slip is toward a runway) would be the alignment of the aircraft, path of movement, and the axis of the runway relative to each other. That difference is so minor, as to not require a distinct term in my opinion. If you are forward slipping toward a runway, there will be a heading but no direction change, prior to landing. If it's a side slip, heading will remain the same, direction will have to be changed.
A slip toward a runway is done to optimize the approach path. We must assume that if the pilot is optimizing the approach path, it's because he/she has the runway in sight. In that case, the pilot is slipping toward the runway! Side/forward... who really cares!
Sorry Shumway, I was not planning to take the shine off your otherwise worthwhile question....