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"Skeet" choke is the least restrictive of the chokes, then improved, modified, and full. There are also extra full chokes, primarily for turkey hunting.
Lead vs. Steel
When shooting lead shot, the more constriction a choke provides, the tighter the pattern will be at a given distance. So, if you are shooting close targets like skeet, you go for a more open choke. One that allows the shot to spread faster works great because skeet is a close in type of target. On the other hand, trap is a game where the targets are relatively far away. A full choke is considered the standard for that.
Another way to put it is that if you take a full choked gun and shoot a large piece of paper at say 20 yards, you may have a pattern that measures 8 inches, whereas the pattern with improved cylinder may open up to say 18 inches. That is a bit of a simplification, but you get the point.
The visual below may be of further use. Cylinder bore quickly becomes useless as range increases. The tighter the choke, the more effective the shot is at longer ranges.
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Today's shotguns primarily use interchangeable, screw-in chokes. These choke tubes are a convenient way to have any choke you want while keeping the same barrel on the gun. Every manufacturer uses it's own trademarked choke system. Remington is Rem choke, Browning is invector or invector plus, etc.
Most of these tubes install flush to the muzzle with a wrench but some extend past the barrel. Some even incorporate muzzle brakes, flash suppressors, door breachers, you name it.
Before the advent of the screw in tubes barrels had fixed chokes. The choke was made into the barrel when it was manufactured. If you wanted a different choke, you generally bought a different barrel.
The only way to get interchangable chokes back in the day was to have a poly choke installed. Poly chokes were fairly popular because they allowed the shooter to literally dial in which choke they wanted.
These chokes are professionally installed onto the barrel by the poly choke company or a gunsmith. While popular once, they have basically been replaced by screw in chokes.