I would argue that a military style handgun is any handgun that can be used in an offensive and/or defensive manner.
Per Kerner the state, or local government can restrict carry on size. The wording as to military handguns has to do with those guns that are not easily concealed. The restriction in Chapel Hill I believe is 8 inches, and that is measrued from the tip of the barrel to the rear of the slide, plus the measurement from the top of the handgun to the heal. Most compacts are according to that restriction legal. The military term used in Kerner was 90 years ago 1921. Before the hype of today.
I believe there are federal rulings also to support that citizens have access to military weapons. NRA brought us this mess with the NFA. and then GCA. Before that citizens had access to all weapons that the military uses. This is the true intention of 2A, not self defense as the courts would have us believe. It is a check against tyranny and for that to be effective we must have access to the same weapons. Not many soldiers are issued or carry a NAA pocket revolver.