There can be a very slight difference between properly fit and not fit properly. It can end up putting inappropriate stresses on the mechanism and prevent it from cycling smoothly and properly. Too much space and it will become inaccurate. This is measured in thousandths of an inch. Sometimes a firearm will wear in to settle into correct fitment when this is small enough. in essence, this is based in the skill and judgment of a gunsmith installing the barrel.
If it doesn't smooth out properly, or you start to see galling in the locking areas of the barrel or slide where it mates you should have a gunsmith address this.
There have been multiple names for the 9mm Luger round we know today. 9x19mm... 9mm Parabellum 9mm Luger.. They all refer to the same round invented for the German Luger pistol which first designed in 1901 and first used widely in 1904 with the Navy model Luger. This pistol was manufactured by Ludwig Loewe's subsidiary company DWM (
Deutsche Waffen und Munitionsfabriken) whose wire cable address was "Parabellum". Georg Luger had adopted the cartridge as a military power caliber cartridge by increasing the scale of the bottleneck 7.65mmx21mm Parabellum Luger cartridge.