There was a distinctino between arms (guns, swords), and ordinance (cannons).
'Arms' seems to entail (as a loose definition) anything that can be carried in 2 arms.
In genarl, Ordinance is the stuff that goes down range, arms are the devices that send it there.
Private ownership of cannon was well known at the time the second amendment was written.
We have never, to my knowledge, made an ordinance control or limitation treaty with another country, we have made many arms limitation treaties. Those all concerned items much larger than small arms, such as battleships. The very term "small arms" indicates that there other sorts. Generally machine guns are small arms, cannon are not , but they are still arms.
There's not much distinction, as citizens have owned MOST of the weapons of war since the beginning. Armed ships were common, and that was what would be used when letters of Marque and Reprisal were issued by the Congress. Also, to this day, some folks own artillery (though the BATFags restrict it greatly) and beltfed weapons. Some collectors even own warplanes. Personally I want most of the above, including an LPH as a yacht. (an LPH is an amphibious assault ship, designed for carrying Marine infantry and helicopters.)