>I frequently hear people use the word "service" as a general term for armed forces. As far as why people ask about the branch, IMHO, it is because in the USA there is a much greater respect for people who serve/served in the military than, for example, in your or my former world. Here people volunteer to serve as opposed to being sent like herd of sheep kicking and screaming. Therefore, I think naming a specific branch of the services shows a certain extra respect.
You can't say "I wonder whether, in case the political system completely fails, the service would take over".