For instance, what are the differences between the concepts like depression, mental health, well-being, happiness, and life satisfaction? Are they synonymous? It is clear that the literature of subjective well-being in economics uses happiness or life satisfaction or sometimes mental health measures such as GHQ-12 as a sort of proxy for the utility. In the terminology of Kahneman, these are all proxies for the experienced utility. What is “depression” in this context?
The existing research suggests that these are all related but independent constructs. Thus, although it may appear, on the surface, that the absence of depression is equitable with the presence of happiness, this is often not the case. All of these variables can be thought of akin to a trait model; thus, they may all be present in greater or lesser amounts. For example, it is possible at the same moment to be very happy and content about a relationship while being very unhappy about a job.... Further, just because one is not altogether happy, does not mean that one is depressed; in other words, they are not bipolar opposites but, rather, just pieces of a complex cognitive-emotional process.
All of the constructs that you mention are related but still distinct. In the literature on subjective well-being, well-being is a broad construct that encompasses many different components, including regular positive affect and low negative affect (the more emotional component or well-being), overall life satisfaction (which is a more cognitive assessment of one's life), satisfaction with various components of one's life. Happiness is seen as a more emotional state and is most akin to regular positive affect. Of course, depression and other mental health problems are negatively associated with well-being; but, as Jameson Hirsch notes, they are not simply opposite ends of a single dimension. It is hard to have high well-being when one is depressed, but the absence of depression is not enough to guarantee high well-being. Ed Diener's book on Happiness provides a great introduction to these measurement issues in well-being research: http://www.amazon.com/Happiness-Unlocking-Mysteries-Psychological-Wealth/dp/1405146613/ref=sr_1_1?ie=UTF8&qid=1396878385&sr=8-1&keywords=ed+diener
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