There are matches, and there are matches...
I recommend watching the movie "My Cousin Vinnie". And pay attention to how the "experts" match the car and its tires.
In a court, what reality actually
is, matters a little less than what the jury
believes reality to be.
The ability of forensics to precisely match a fired bullet (or case) to a specific gun depends on the gun having something unique that can be identified.
General matches are much easier. The rifling marks are easily identifiable in that regard. For example, a .38 caliber bullet shows rifling with a 1 in 14" twist. This is the twist used in a Colt. The suspect/defendant owns a .38 revolver, but its a S&W. S&W uses a 1 in 18.75" twist. The bullet in evidence could
not have been fired by the defendant's gun. That's a general ID.
If you have the right type of gun to have fired the evidence bullet, THEN it becomes a matter of whether or not the exact gun did fire it. And that needs some kind of unique mark that only that gun puts on the bullet. Not nearly as easy to do as it sounds like on TV.
Now, with a shotgun, its a bit of a different story. And only partly because of the lack of rifling. Everyone who doesn't already know shotguns don't leave rifling, and so cannot be "matched" will be told that, by the time they sit in a jury box.
So, the prosecution doesn't even try. And they don't need to. What they need to prove is that you had motive (a believable reason), opportunity (no vaild alibi) the murder weapon (here's where it gets you). All they have to do is prove you had a shotgun. Because of what everyone "knows" they don't have to prove it was your shotgun, they way they would have to prove it was your S&W pistol) only that you HAVE a shotgun, which is enough for nearly any jury to accept.
In many ways, using a shotgun to commit a crime actually makes it easier for them to get a conviction, despite the fact that many think it makes it harder, because "there's no ballistics" to match. (and yes, as was pointed out, "ballistics" is the wrong word to use, but its done all the time on TV)
ALSO, its not an absolute requirement that the cops physically have the murder weapon (or even the body!
). Sure, makes it tougher to prove the case, beyond reasonable doubt, but not impossible. In the end, what it boils down to is whether or not the jury gets convinced (despite what reality actually is) to convict.
Another fictional account is in SHAWSHANK REDEMPTION. The main character in it gets convicted of killing his wife, despite the fact that the cops never recovered his gun. While the movies I mentioned are fiction, they illustrate the kinds of things to sometimes do happen in real life, to real people.