No. After all you are firing the bullet through a RIFLE. What does that mean? Exactly, the barrel has rifling, which causes the bullet to spin for better stability. In order for this to happen, the bullet has to be a little bit larger in diameter, and then as it travels down the barrel gets squished and rotated.
That is the reason why barrels get so hot after firing bullets.
So the caliber is actually the smallest diameter of the barrel, so a M16 for example should have a barrel diameter at the narrowest point of 5.56mm. After firing a lot the barrel can actually get wider. In the German Army, the maximum tolerance AFAIK is 0.01mm, so if 5.58mm would be measured, the barrel will get replaced.
This is also the reason you should not fire you (military) rifle with the flash hider, since it also makes sure the front end of your barrel does not "split" open.