I believe both are real, seeing chemical reactions happen to the body once someone is suffering from either or both. Certainly though, it can kinda be "made up", especially anxiety, seeing that it surges from possibilities created from your own mind and your fear upon these, but nonetheless they are mental illnesses and they need special treatment.
If i was to explain both depression and anxiety in a more simplistic way, they are basically a set of feelings playing at the same time. Like depression being a long-term sadness and melancholia feeling, while anxiety is a long-term fear and worry feeling (really resuming it up).