The parameters of shotgun design are gauge, choke, barrel length, and shell. These parameters interact, so their ultimate effect on performance can not be isolated.
Gauge refers to the inside diameter of the barrel – the bore. Shotguns are normally smooth bore (not rifled). There are four common gauges, ranked from small to large: 20, 16, 12, 10, where the number refers to the weight, in fractions of a pound, of a solid lead ball with the diameter of the bore. Thus a 16 gauge bore ideally passes a lead ball weighing 1 ounce. Of course, shotguns do not ordinarily fire such projectiles; it is a metric inherited from cannon design. One shotgun bore size does use a caliber designation, the .410, which is a smaller gauge than 20 gauge.
All other parameters held constant, a gross characterization of the practical effects of each next larger gauge are: the gun is 8 ounces heavier; the range is 5 additional yards; the shot string is shorter; a more powerful recoil (kick) is transmitted to the shooter’s shoulder. A 16 gauge shotgun has an effective range out to 50 yards. In the American market, the 16 gauge was mostly dropped from production in the 1970s, so that 12 and 20 gauge are by far the most available shotguns today.
Shotgun bores are not cylindrical. The chamber, in which the shell is fired, has a larger diameter than the bore, to accommodate the shell’s paper or plastic jacket. The forcing cone between the chamber and the barrel then restricts the shot string to the effective bore of the barrel. At the muzzle end of the barrel, there is optionally a further restriction called the choke, which affects shot concentration at the target. The shot pattern expands when it leaves the muzzle and at the target has a Gaussian distribution. Barrels without a muzzle restriction have no choke. Barrels with full choke have a 0.35 in. constriction. A commonly used choke is called ‘modified’ and has a 0.2 in. constriction. The practical effects of different chokes relate to the percent of shot delivered to a 30 in. circle at 40 yards. It ranges from 40% to 60% to 70% for no choke, modified choke, and full choke respectively. Only a fraction of the shot is needed to intersect the target to achieve the desired effect, and there is more chance of that with less choke (shot concentration). Thus, those of us who are not fully competent with aiming will have more success with less choke. My M37 has no choke.