When danger is lurking and threatens us, we must know to run to safety before it is too late. Save your life, in sheltering games!
In the latter, the scene changes and the hero or character you control are not necessarily in the right place. He must reach as fast as he can a new location where it will remain safe and comfortable.
In Rektagon, for example, you'll need to show a lot of skills and dexterity to put your character in the right place before the decor is closing in on him.