I would say unhappiness occurs more through your current circumstance and something that might be persistently wrong with it. As someone said, it could be because of not being satisfied in a specific job or relationship.
Depression, on the other hand, has a much more widespread effect, as it can stop you from enjoying things you normally enjoy and make you lose interest in things you've been doing for a long time. This definitely hit me in my last year of my undergraduate degree and I ended up doing things like going to social occasions just to satisfy other people and then leaving before the end without anyone noticing, and not being very good at managing my time and work (much to the annoyance of my MMath dissertation supervisor, who mistook depression for unhappiness and didn't really understand it).
One thing I think needs to change is people's general understanding of depression and that it isn't just a matter of being "a bit sad". My parents have sometimes dismissed my depression as being "under the weather" and things like that, either because they don't fully understand depression or just because it makes their lives easier by assuming that.