My understanding is that, in the terms used at the time of drafting and ratification, “arms” meant any weapon that a common foot soldier could carry into battle, whereas “ordinance” is a reference to heavy weaponry, such as canon, which a common soldier could not carry into battle ...
Therefore, this would exclude any American citizen from, er-uh, “keeping and bearing” an Abrams Tank ... However, I see no problem with a 30 or 50 cal machine gun, bazooka, mortar, etc - since any of those could be carried by a common foot soldier ... Well, OK, the 50 cal would be a rather heavy piece of “arms” to carry around, unless you’re Rambo.
"To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water; "