The .22 rifle cartridges used to kill Pat and Sheldon were "rimfire" rounds, which have the priming in the rim of the casing. To ignite the powder in the casing, a firing pin hits the rim, leaving an imprint. This imprint shows what type or shape the firing pin was, and this in turn helps to identify the type of weapon was used. Also, marks can be made on the casing which show the imprint of the bolt face, or scratches might appear from the loading mechanism or the extractor/ejector.
A bullet which has been fired from a rifle or pistol will have rifling marks on it which also help to determine the type of weapon used. These marks on bullets and on spent shell casings can also assist in the identification of a specific weapon when compared with a test cartridge fired from a suspected firearm.
Rifle or pistol barrels could have anywhere from 2 to 16 grooves and lands in them. These are spiral cuts which impart spin and stability to the bullet while in flight. These marks are like "fingerprints" to ballistic experts.
The general measurements and number of grooves help to determine the type or make of weapon that was used, but included within the rifling marks are very specific/unique scratches and marks made when the bullet passed through the barrel and which can help to identify the exact weapon which was used in the crime.
Bullets, casings, and unfired cartridges might also contain further evidence, such as DNA and human fingerprints which can help to link the murder weapon to an individual.
The study of wounds made by bullets can also yield clues as to method and actions of the killer.
Thanks, Richard. The photo of the firing pin impression is very helpful. It's easy to see how LE could use that information to identify the specific weapon that was used in these murders.