The Remington Model 870 Police Max is a U.S.-made 12 gauge shotgun manufactured by Remington Arms Company, Inc. It is widely used by U.S. police and the U.S. military.
The 870p is a variation of the standard Remington 870 Pump Shotgun produced in 1950. The design itself was based on the Model 17 Shotgun designed by John Pederson and John Browning. The 870p was released specifically for use by Police and Military personnel.
It is unlikely that John Connor's single pistol shot did any serious damage and was probably just used for dramatic effect.
Correction the shotgun used by Cameron was a semi-auto and as Remington 870 are by definition pump action, this cannot be the same gun. However, superficially, they do resemble each other. The gun used by Cameron is most likey a tactical model of the Remington 1100 or 11-87.