What is the difference between a tail slide and a whip stall?
A "tail slide" occurs when an aircraft is nose up and loses all forward airspeed. Gravity then pulls the plane "backwards" towards earth.  The "whip" occurs when a sinking aircraft is flipped nose down by the airflow as it assumes a more aerodynamicly stable orientation.

Aircraft will generally nose down when they sink due to more area behind the center of gravity than ahead (as viewed from underneath the plane).  The horizontal stabilizer, farthest from the CG, is the main contributer, especially with down el.

Note that with canard and delta designs, it is the back of the main wing serving this function.

The issue is that when one tail slides, the increased vertical sink rate turns a gentle nose down into a hard "whip", greatly increasing stresses on the aircraft.  There for it is imperative to make sure the plane can handle this and not to tail slide too long.

For hang gliders and "flying lawn chair" type aircraft, a hard whip can be induced by pulling forward too aggressively in stall recovery (deltas have big tails), resulting in a full blown forward tumble.

Definitely something to discuss with your acrobatics instructor.