After a unit moves, it 'stops' when there is no additional movement for that unit on the storyline (or if it's being carried, no additional movement on the storyline for the unit that's carrying it). A unit must first move to then stop. Projectiles are similar; if they do not enter a new location, the projectile hasn't moved at all and thus cannot stop. For example, a Snowball that doesn't enter any new locations and doesn't move will not deal any damage. Note that 'stops' is not the same as at rest. As a complicated example, consider casting Blink with an Orb of Ba'al Berith nearby. Both Blink spells will be on the storyline. After the first Blink resolves, whatever unit just moved will 'stop,' since there's no other movement for that unit on the storyline immediately after the first Blink resolves; the ally for the second Blink hasn't been chosen yet. If the same unit is chosen for the second Blink, it will stop a second time (assuming it changes locations after each Blink to actually result in movement).