There are several reasons why tags are stolen, sometimes they are driving an unregistered vehicle and steal a tag rather than register it, sometimes tags are stolen to be used on stolen cars, so while the Police might be looking for a certain description with a specific tag number, if they switch tags or steal a tag, sometimes they can get away with it, of course if the Police run the tag, if it's been reported stolen it should come up that way on the computer.
A smart criminal will find a tag that matches the description of the stolen vehicle, say they steal a white Impala, if they are smart, they will find another white Impala and switch tags, often the owner of the car won't notice the tags have been switched and won't report it, and if the Police run the tag it will come back with something that will pass for the right model. It's been a few years(!) since I was in law enforcement, back then the State of Oklahoma didn't keep track of vehicle colors, many other states do, that's helpful for the officers as long as it hasn't been repainted a different color.