Dumb Question...
 

When one talks about the FAA Medical Exam, is this the same thing as the First Class Medical Exam, or is it a separate exam?

Yes.

Filler.

Thank you!

Or the Second Class or the Third Class.

There are three different types of FAA Medical Exams.

First Class: Required for operations that require and Air Transport Certificate.

Second Class: Required for operations for hire.

Third Class: Required for operations that require only a Private Pilot Certificate.

This is an Airline Pilot forum, so "First Class" and "FAA Medical" tend to be used for the same thing.

I would suggest always getting the first class. I have seen applications that ask if you have maintained the first class medical and the lapses between your medicals.

FWIW, one Senior AME's opinion was that in a close case the FAA is more likely to renew a current first class than to "upgrade" a second class to a first.