If you don’t mind me grossly oversimplifying, this one’s pretty easy.
Police are trained to subdue their opponent. The military is trained to kill their foes. Obviously SWAT teams and other paramilitary police units muddy this a bit, and some military personnel are trained in police techniques because their job requires it.
Modern police forms are an omnivorous amalgam of dozens of different traditional martial arts. You’ll see bits of Judo and Jujitsu, along with a lot of other influences.
Modern military forms have evolved from classic boxing and wrestling (as in the kind of grappling you see out of high school wrestling, not “professional wrestling”) techniques. Everywhere modern military forces have gone, they’ve incorporated some of the practical, local techniques, and developed or appropriated counters for those same techniques. For US Forces, that means a lot of traditional Asian and European styles have contributed something.
There’s also a lot of crossover between the military and police styles. A lot of ex-military find jobs in law enforcement, bring their training with them and share, and increasingly military forces have had to pick up law enforcement related duties, and the related hand to hand techniques.
You can find plenty of videos on both military and police techniques online. MCMAP (Marine Corps Martial Arts Program) will get you the videos on the Marine techniques, while Police Hand to Hand training should get you a decent sampling of police techniques.