Every checkup includes a cleaning so they're usually used interchangeably (at least everywhere I've lived in the US).

Dentists don't usually do any of the cleaning, that's the job of the dental hygienists.

I don't know what to tell you. Every 6 months I go to the dentist. They do all those things. They bill my insurance. I pay whatever is left over.

Yes yes, I got it :) Was just curious about the different approaches.