Originally Posted by Pet_Sounds

Yeah, there's a difference in equations. Calculus was invented basically for this question. You need an "open interval" (which can be arbitrarily small) of time around a given point to discuss instantaneous rate of change, and the difference comes down to the behaviour of the object in that open interval as it approaches the point you're interested in. In the case of the ball in mid-air, its motion changes immediately before and after the point in time at which its velocity is zero; the ball on the ground doesn't move at all.

Sorry I'm not explaining this very well, it's hard without math.