Example of 'muzzle velocity' in relation to accuracy. This antique gun was used in war. War. Not hunting.

The Caliber of a gun is determined by the 'diameter' of the bullet / shot / ammunition. The word sounds very much like the word caliper. Caliper is a noun. Below right is an actual caliper.

The caliber of a gun is measured in mm. 

So, when a gun is identified as a 45 or 38 it is an OLDER measurement. When a gun collector states he has a 45 it is 45 hundredths of an inch.

Why is a 45 better than a 38? Because the 45 can hold more FIRING POWDER and increase the trajectory of the bullet / shot / ammunition. The more powder, the more higher / accurate the 'muzzle velocity.'

Today, there are many guns measured in mm (millimeters). ie: 9mm which is used by most law enforcement officers in 2013.  

Every one mm = 0.0393701 inch. 

A 9mm is a little less than a 36 caliber. A 9mm is 0.354 inch diameter. Rounded out it is .35 inch (stated it is 35 hundredths of an inch). The 9mm holds less gun powder than a 38 or 45.
Some of the explosion in the chamber of the 9mm handgun goes into putting the next bullet in the chamber; ie: semi-automatic. The muzzle velocity of a 9mm is at least 390 meters per second but with as much as 435 meters per second. The muzzle velocity of a 38 is 679 meters per second but with as much as 980 meters per second. The variation in the speed is due to the type of powder in the ammunition / bullet /shot.

The reason the 9mm is preferred in police work over a 38 is the rapid fire capacity of the gun, not necessarily the lethality or accuracy of it. Okay?

That will help round out the understanding of the 'dynamics' of the guns limited by the Assault Weapons Ban Bill.