"Arms in the hands of the citizens may be used at individual discretion for the defense of the country, the overthrow of tyranny or private self-defense."
Arms in the hands of citizens may be used at individual discretion, not State government discretion, individual discretion. To arrive at your interpretation of the first John Adams quote, you would have to conclude that he changed his mind about the subject sometime between the two statements.
You individually decide whether or not you are willing to take up arms "for defense of the country, the overthrow of tyranny or private self-defense." Carry a concealed weapon in violation of state law and land in the pokey, per Dead Corpse's beloved Nunn decision.