Would work a 7.62x39 caliber on a rifle that uses a 7.62 x50 NATO?

i don't understand what x39 x50 x etc mean or NATO i just know that NATO is an army alliance , and sometimes its hard to find the different calibers , would one of those work ? ooh and the rifle that i want to use in the 7.62x39 is a FN FAL . please some one answer !!!!