The speed of a bullet does depend on the gun, but there is little change in statistic terms, but it makes a lot of difference when it hits something. Also the size of round affects the speed, a 5.56mm round goes faster than a 7.62mm round for example.
Even with that most bullets go around, and above Mach 1, but only just. Depending on your altitude it changes what speed (mph or km/h) Mach 1 is, but it is still refered to as Mach 1 even if at sea level it is 760 mph but at 20,000 ft it is 730 mph (not the real figure).