I read that you can power the Arduino Pro Mini with a battery by connecting the battery to the 5V pin, bypassing the regulator.

Somewhere else I read that the only difference between a 3.3V and 5V Pro Mini is the regulator.

Are these assumptions correct? If yes, can I use a 5V Pro Mini like a 3.3V by powering it with a 3V Battery on the 5V pin?

updated: I want to run the 5V board at 3.3V.

(I can get the 5V version cheaper)