When I send a recommendation request, does each REU request a different "style" of rec letter?
Before you put their name down, email the professor again just to make sure they're still ok to write the letter.

Once they've agreed, don't worry about the different formats that may be required for different places. Professors are generally fully aware of what the letter writing process demands and would not (or at least, should not) commit to it unless they know they have time for it.

In your initial email, it may be a good idea to list the places you're applying to and their respective deadlines, so the professor has a rough idea of the time commitment.