Do they use different terms for the coverage in different states?

In the places I've lived, you have to have what's called liability insurance at a minimum, and that's the one that covers other people's property but not your own.

Around here, collision coverage is to reimburse you for damage to your own car/property in the event of an accident (collision with another vehicle), and comprehensive coverage is to handle some of the other non-collision damage (like from hail).