Cannot speak about motion, but in surface continuity you will also look at higher "derivatives" if you want really really smooth transfers between two curves. So you make the transition of the curvature comb of a curve's curvature comb tangetial or so. There they just call the transitions g0, g1, g2, g3, g4 and so on.

I cannot judge whether snap, crackle and pop are things people actually use when they talk about those derivatives in motion.