This may seem a tad on the simplistic side, but I prefer straightforward answers to straightforward questions, such as this one. There are any number of theories about the difference between the two, but it really comes down to this simple solution:
On a related note:
Of couse, this is for the United States Military, other contries might have other conventions. This list also does not take into consideration all the little pet names members of one branch have for members of another. I won't go into them, first, because I only know a couple, and second, because a lot of them you can't use (without getting hurt) unless you're military. (Example, don't ever call a Sailor a Squid unless you're a Marine! 'Cause a squid is just a lower form of Marine life!) 2
Airman is also a rating(job title) in the Navy, for someone who works on Navy Aircraft. But in this case, they are Sailors first, Airmen second.
2 I was told so by a former Marine.