The pattern of spiral grooves cut into a weapon's barrel (rifling) will leave an impression on every bullet. Barrels are made of steel, and projectiles are made of softer metals like copper and lead.
Forensic labs can recover bullets and study the rifling impressions. In general, they should be able to tell which manufacturer made the gun that fired that bullet (each company uses their own technique & pattern for rifling). It is possible to narrow the gun identification down even further by looking at microscopic differences in the groove impressions.
If the forensics lab has the suspected firearm used in a crime, they can pretty much prove whether it fired the bullets in question to a high degree of certainty. Its basically a gun's fingerprint.
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