The Guard is only the militia, or part of it that is, when serving in their state role. Once they are federalized, they are part of the Army or Air Force. We say they are "dual hatted". In point of fact, all Guardsmen are members of the reserve of the appropriate federal service, as well as members of the National Guard of their state.
When I became an Air National Guardsman, I did not need to get a new ID card, as the ID card was the same as I carried as an Air Force Reservists. I did need to take a new commissioning oath, to the state as well as to the federal Constitution.