If I'm not misstaken, tropical lobsters don't have the nice claws that the cold water cousins do.
You are correct sir. They are commonly referred to as spiny lobster or rock lobsters. Most tropical areas have them and cool waters as well. Southern California is actually a good lobster region, but most get sent over seas to Asia and they aren't really marketed as much except in San Diego. Even more expensive than Maine lobster.
When I lived in Maui, we would dive for them, but only with snorkels. Illegal to use tanks. Their antenna stick up out of the coral and we used steel mesh gloves to reach in and grab them. Gotta watch out for eels and other critters!!!