While the two are different - opposites, in some ways - they very frequently coincide and feed into each other circularly. They're also extremely common and can be overcome through therapy, possibly combined with medication. If you're dealing with them, know that it's okay and normal, and see if you can find a therapist to talk with.
Depression is when I don't want to get out of bed because I feel everything is pointless and hopeless. You are waiting to die because you are not motivated to do anything. Instead of being over-stimulated, you are under-stimulated.
For me, anxiety can trigger depressive episodes, but not vice versa.