All 9mm Parabellum, 9x19mm, 9mm Luger, 9mm NATO cartridges are the same dimensionally and should fit in modern 9mm guns and be safe to fire. Know that other 9mm cartridges and firearms exist, but they should all be labeled as to what they are. Do you have a specific ammo and firearm in mind?
All 9mm Parabellum, 9x19mm, 9mm Luger, 9mm NATO cartridges are the equivalent correspondingly and ought to fit in present day 9mm weapons and be protected to shoot. Realize that other 9mm cartridges and guns exist, however they ought to be generally named with regards to what they are.
What we typically call 9 mm (in the USA), I wish we would standardize that and call it 9x19. For one, it is very descriptive of the cartridge with 9 mm diameter and 19mm for the case length. Secondly, it wouldn't get confused with 9x18 which is a different 9mm critter. I work in a gun store and every once in great while we get some 9x18 ammo in to sell and every once in a great while somebody with a 9x19 buys it. That stuff is used mostly by eastern european built hand guns. From what I've seen, when mistakenly put into a 9x19 handgun, the 9x18 cartridge won't chamber although every once in awhile a round may make in and it will go bang. I'm guessing trying to put a 9x19 cartridge into a gun designed for 9x18 won't work at all but I have not seen anyone do that either on purpose or by mistake.
I own several CZ 75B pistols and shoot them competitively. A few years ago a friend had a chance to buy a 75B at what seemed like a bargain basement price. Since I own a few, he wanted to know if I thought it was a good deal. All I had to go by were some photos he had of the gun. From the photos the gun looked like it was in fantastic condition. At first I told him, if the gun is also in good working order, as it appeared to be in the photos, to jump on the deal. However, to make a long story short, upon closer exam, I noticed it was chambered for 9x18. I advised him to walk away from it because, as enticing as the price was, ammo availability and ammo cost could be a problem.
Edited to add something re: that 75B I advised my friend not to buy. I'm not enough of a gunsmith to know but perhaps he could have dropped in a 75B 9x19 barrel and possibly a different recoil spring too and everything would have been a go. I just don't know if something that simple would work or not. Not sure about the magazines working either.