I think of Bermuda and the Bahamas as more "Floridian" islands because technically speaking they are in the Atlantic Ocean. I've sailed to them from Florida on private boats in the past as well as on cruise ships but I never considered them as the "Caribbean".

I'm surprised sometimes when I see cruises to those spots being billed as a Caribbean Vacation.  Not that they aren't great islands to visit BUT they aren't really the Caribbean ...