If the movement is illegal in itself, it's a false start -- if the lineman was moving from a three point stance to a two point stance, or if he moved quickly in a manner that simulated a snap, for instance.
If the movement itself was not a foul, but only became a foul because it did not end prior to the snap, then it is an illegal shift. That is to say, if the snap was two second later you'd have no foul on the play due to this shift, it's not a false start.