also: motion · shift · in motion · shifting
Both are pre-snap movement and they are not the same thing. A shift is a move from one set position to another; motion is continuous movement that can still be happening at the snap. The difference is a rules difference, which is why it gets flagged.
A player moves continuously before the snap and can still be moving when the ball is snapped. In American football this is limited to one player at a time, and the direction he is allowed to be moving at the snap is restricted, which is the part that produces penalties.
What motion buys an offense is information and leverage at once. It forces the defense to respond visibly, so the offense learns something about the coverage. It puts a player somewhere the defense did not align for.
in motionshift, tradeA shift is a move between two stationary positions. Any number of players can shift, which is what distinguishes it from motion, and the offense must be set again before the ball is snapped.
A whole-formation shift changes what the defense is looking at completely. It does so late enough that a defense which has already communicated a call has to redo it. That is the point: a shift attacks a defense's communication rather than its alignment.
shiftingmotionCoaches sometimes use motion loosely for any pre-snap movement, but rulebooks distinguish a shift from a player still moving at the snap. Set times, legal direction and how many players may move differ by level, so teach the current rulebook for your team.