From Internet Movie Firearms Database - Guns in Movies, TV and Video Games
If you want an answer to why, by the way, there's a couple reasons:
- A fair few of our founding users are of the age where their main references are Cold War-era books and documentaries: in these, these aren't just the NATO names of these systems, they're often the only names given to these systems (mainly because the GRAU designations weren't widely known in the West). As a casual example I have a book from 1983 called Rockets and Missiles of World War III which will only ever use the NATO reporting name.
- The AT-(number) system is much, much easier to remember than the GRAU inventory code. I could tell you the NATO names from memory (which, when you think about it, isn't surprising since that's the whole point of those codes), I doubt I could manage a single one of the GRAU codes.
- The AT- codes are kind of convenient in that they can be used to refer to the missile or the system as a whole without being any less correct: the GRAU designations applied to the systems in various sources are much more confusing. AT-3 is usually referred to by the GRAU code 9M14 which is the code for the missile, AT-4 is 9K111 which is the entire system, AT-5 is 9M113 which is the missile, AT-13 is 9K115-2 which is the entire system, and AT-14 is 9M133 which is the missile. I have no idea why it works that way.