Time Spiral is full of themes of the past. Premature Burial kills a creature that has come into play a turn ago—a spell that destroys creatures “in the past.”
Planar Chaos’s themes are about the alternate present. Cradle to Grave kills a creature that came into play this turn—a piece of removal usable only in the immediate present.
Future Sight is all about the future. Grave Peril isn’t an instant or sorcery; it is an enchantment. It sticks around until it finds an adequate target. In effect, when you cast it, you’re killing a creature that hasn’t even arrived yet—a spell that reaches “into the future.”