Originally Posted by
unemployedagain
sideslip uses opposite aileron and rudder while forward is the difference of the wing correction angle as compared to track, no inputs just correcting for wind with a heading change to course.

One thing (among others

) to clarify: A "crab" is not a slip and has nothing to do with a slip. A crab is =coordinated= straight and level flight.
Don't worry about the names of the two slips. I've heard people try to explain why they are called what they are and you can go nuts trying to figure it out.
rickair pretty much nailed the explanation: a slip is a slip - aerodynamically, they are all the same. What the slip is called is related to what the slip is being used for, with a "forward" slip used to lose altitude and a "side" slip used for landing in a crosswind.