Was your cat's death more of a surprise than your grandma's?
I've noticed (only after that strangely wise kid on The Cleavland Show pointed it out) that it's possible to grieve for people while they're still alive. If someone is ill and you think they might die, you start grieving early. You also feel a lot of anxiety about their possible death, especially if you feel like you can or should do something to improve the situation. Depending on the exact circumstances, you might even adjust to their death almost completely before they die, and when they do die, it's actually kind of a weight off your shoulders. On the other hand, if someone dies very suddenly, all the grief hits you at once. Some situations are a mix of those two scenarios.