Question about purchasing handgun ammunition?

Well I had heard but never knew from personal experience (as I do not own any handguns) that to buy handgun ammo, you must show information, etc like a pistol permit (for states that require it). I happen to live in New York. So I was thinking "What if I was handed down a 9mm carbine?" as an example. Are you telling me that I couldnt buy ammo for it? Just a thought. Thanks for any information you can give me.