Technically, if a minion heals, its wounds can go away. If a minion gains life, there's no effect. But there are very few cards in the game that ever heal minions, e.g. . The vast majority of healing effects only heal "you," the player.
Drag. Pull.
Note that "Lure" is different, since "Lure" requires the unit to take the step themselves.
Note that "leave" and "enter" obviously care about different locations, but the moment in time is identical. If you move and leave one location, you have simultaneously entered a different location. There's no moment when you're in limbo between locations.