The bullet is the part that comes out of the gun at a high velocity....You know, the projectile..... The entire thing, case, powder, bullet, primer is a cartridge.
Even when found in a school.
(Plus, placing the schools on LOCKDOWN? Really?)
The educational administrators must be total idiots.
Add in the fact that the police chose to bother to do a search. Unless it was just a chance for overtime or to use their Autoriteh!