I'm almost positive any of the military stuff that can be traced to ignition pads, primers, or expulsion charges, that is labeled "black powder" of one class or another by the military, is potassium-nitrate-based, but the composition is a fair question to ask anyone offering you black powder.
The sodium nitrate based stuff is called "blasting powder" and the grains are rough like crushed gravel.
I've had 2FA "blasting powder" here that's sodium-nitrate-based, we did try it in larger cannons as blank charges, but it is verrrry slow burning and as I recall it didn't work well for us. I'm not aware of any particular danger in using it other than it doesn't do much and I think I wasted my money on it. No one that I know of tries to use it to propel projectiles, it is not considered acceptable for that. If anyone has more info, let us know please.
The grain size on the military powders, again, are not uniform, but consist of a range of grain sizes that screen as I indicated above. If anyone knows the screen size specs for commercial "cannon" grade powder, post it here, and we can compare the military powders to it.