Both kinds are available. My BR player remote (for the PS3) has two separate menu buttons, one which is supposed to call the main menu, leaving the movie and another one which is supposed to call the menu that overlays while the movie continues to play.
Unfortunately some Blu-rays disallow either button, so it may simply not be possible to go to the main menu while the film is running (then sometimes clicking the other button will do that
) and others don't have an overlay menu and you must go to the main menu. It seems inconsistent and is therefore very confusing and irritating.