They’re all mailboxes. So are the blue U.S. mail receptacles in public places where you can deposit your outgoing mail. It’s a term that embraces a broad category, like, for example, clock and house.
A mail slot may or may not be associated with a given mailbox; and you can have a mail slot without a mailbox, as for instance, when the mail is dropped through a slot into a chute in a hotel, or enters your home by falling through a slot in your door and landing on the floor.
The interesting part, I think, is that any enclosed receptacle explicitly dedicated to containing mail is called a mailbox; but what is mail? From the public’s point of view, it’s pretty much only mail when it is in, or is about to be in, or has just been in, or is being processed for deposit in, a mailbox. Its status as mail is situational and transitory; it’s the relationship to a mailbox that makes it mail.
I don’t know how those terms are used within the postal service, so I’m speaking only of their common use.