Since one was originally just a shortened form of the other, there shouldn't be a difference. In common usage, there is, but all it does is cause problems. I'll still use them more or less interchangeably, because nobody can ever agree one what they mean anyway. Go to ProgArchives, or the YesFans boards, or the Genesis Talking Shop, and ask if there's a difference, and you'll get 10 different answers when you'd think you'd only get two. Then ask for the definitions, and you'll get 100.
Prog/Progressive can mean a certain genre, or a certain style, or a certain "attitude" about the music, none of which are exactly the same and none of which depend upon when the music was made. But it can also point to a specific time period (some people say "prog" when what they really mean is "70's prog" for example) or even a specific movement ("70's prog" for example, which wasn't even called that in the 70's).
There are bands today which are called "progressive" because of their approach to music; they sound nothing like 70's prog. There are bands today which were actually 70's prog bands which are no longer progressive.
The term isn't outdated or overused so much as it's just too general and has too many definitions to have any real meaning. If you use it, you then have to qualify/clarify what you mean anyway. If anything, it's a broad category which you then narrow down to what you "really" mean.