First off, they can’t. The best they can do is say “a gun like this fired the bullet”
There’s a couple of steps involved. Guns fire different kinds of bullets. Some are long, some are short. Some are fat some are skinny. Using the combo of length, width, weight, and a couple of other things they can narrow it down to a few kinds of guns. Its kind of like using a tire to narrow down to a type of car. Different sizes of tires fit on different cars.
Each type of gun has a different style of barrel, most have something called rifling. That’s a set of grooves that spin the bullet so it goes straighter. There’s a different number of grooves, different depth, and different spin for different guns. That can narrow it down even further, either to one gun or a set of guns that use the same barrel.
But like tires this only narrows it down to a range of guns. With modern manufacturing there aren’t enough differences to reliably know which gun fired the bullet. Just like knowing that a car with a Michelin XGV size 75R14 tire narrows it down to a GM car you can’t tell if it was a 64 Skylark. You need additional information that’s not part of the tire to know it was actually a 63 Tempest.
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