So I'm reading a 640+ page book called "The American Rifle" and this question popped into my head for some reason...

Can someone explain to me what is the legal and technical difference between a rifle and a shotgun as could be used in a court of law?

Lets put this into a story problem for some context..
A DNR officer approaches you in your deer hunting blind and says you're hunting with a rifle in a shotgun only area.. You say, "But sir, this is a remington 870 shotgun".. and he says "No, a shot gun fires a bunch of pellets.. not a bullet.. Rifles fire bullets.. shotguns fire groups of round balls.. Come with me cupcake! You're under arrest."

Now, how do you explain to a judge or a jury that your weapon, a Remington 870 slug gun, which has a rifled barrel and loaded with a slug that is propelled by a sequence of events where a firing pin ignites a primer in the center of the shell that then ignites the main propellent, is in fact a shotgun and not a rifle?

Sounds like a rifle to me...