The difference is that The Military is under the direct control of The President of The United States.change the patches and boom, whats the difference? besides the skill level? certain police teams are paramilitary units if ive ever seen one. they intentionaly skirt the law by claiming to be police when by their actions and looks its clear they think they are the military and the guardians of freedom,
Posse Comitatus was promulgated to prevent the POTUS, who is Commander In Chief of the Military, from taking control of the Civilian Police Authority and enforcing Martial Law.
It's part of the "Checks and Balances" enacted in our Governmental system to ensure that a Military dictatorship isn't allowed to take over.