What's the Difference Between an Astronomer and an Astrophysicst?

Given the below rant, I know someone is going to ask because I tend to use the terms interchangeably.

Technically there isn't much of a real difference, it just tends to be how you self-identify. Is it Radio Astronomy, Radio Astrophysics or Gas-Phase Quantum Chemistry? It depends on how you went through your career. A loose rule of thumb tends to be, if you're looking at it, it's astronomy, if it involves a lot of math and not many observations, it's astrophysics. However, I can't think of an example where this comes down one way more than the other. This may be my lack of imagination.

Here's a better way of demonstrating the difference:

If you walk into a bar and you feel cranky and want to be left alone while someone is trying to chat you up, tell them you are an "astrophysicist". The conversation sill stop, you will get a look like you just might be an escaped mental patient (maybe a violent one) and you will be left alone. If you do it right, you may not even be served any more.

However, if you are in a cheerful mood and feeling gregarious, tell people you are an "astronomer". People will ask you all sorts of questions, talk to you, buy you drinks and occasionally, beautiful members of the opposite sex will come up and start kissing you at random (this has happened twice to me, and yes there are witnesses).

That's the difference.