On dog tags “RA” means you enlisted; “US” means you got drafted.
You asserted that we’ve had a standing army since the US was founded, and that is not so.
Im going to guess that both of you are veterans and served before 1970, making you both about 72 or older.
What you are describing I believe disappeared around 1970 at which time the army began using social security numbers instead of issuing their own id numbers.
From Wikipedia:
After the war the Continental Army was quickly disbanded as part of the American distrust of standing armies ... However, because of continuing conflict with Indians, it was soon realized that it was necessary to field a trained standing army. The first of these, the Legion of the United States, was established in 1791.”