From the handling, I see side and forward slip as just names. I got my PPL on an aircraft without flaps or airbrakes. Most of my flying has been on an aircraft with airbrakes, not flaps. I can stop a slip without taking my hand off the throttle, so I seldom used the airbrakes. Only recently did I encounter the term "forward slip".
The distinction is like that between "Stop:sign-braking" and "Red-light-braking" which I don't think driving instructor has ever taught.
