I suffer both, and yes it's at times hard to differentiate.
This is how it was explained to me: Depression is the feeling of loss. You feel defeated and discouraged because of something bad that's already happened. Anxiety is the feeling of fear. It has to do with the future.
Lately I have been dealing with considerable anxiety, but I think this anxiety didn't come out of the blue. The question is that I wasn't truly aware of this anxiety because sometimes it is not easy to differentiate between depression and anxiety symptoms. In CBT I am starting now to introduce anxiety feelings and to rate them as best as I can.