Difference between “bad” and “poor”

Both "bad" and "poor" have several meanings. Oxford Dictionaries Online list eight different meanings for "bad", one meaning being "of poor quality or a low standard:" for which they give these examples:

a bad diet
bad eyesight
a bad listener

Similarly they give three meanings for "poor", one of which is "of a low or inferior standard or quality:" with the examples:

many people are eating a very poor diet
her work was poor

I would say that in these meanings (but only these) they are nearly synonymous, with "poor" perhaps being a softer option. "Your test result was rather poor" doesn't sound quite as bad to me as "Your test result was rather bad". It seems to me you could substitute "poor" for "bad" in all the examples above, but I'm not so sure about the other way round.

But of course that leaves another seven meanings for "bad", and two for "poor", where they are not in the slightest synonymous. And one of those meanings of bad, for example, is "lacking or failing to conform to moral virtue"

The bad guys - morally bad
A bad boy - badly behaved

And surely the first meaning that comes to mind for "poor" is "lacking sufficient money to live at a standard considered comfortable or normal in a society" - nothing to do with "bad" at all.

http://oxforddictionaries.com/definition/english/poor?q=bad
http://oxforddictionaries.com/definition/english/poor?q=poor

I think of bad as being, well, the opposite of good (at least for this discussion). I tend to think of poor as meaning something more like ill-suited or prehaps lacking. I would suggest that even when they are synonyms, poor's meaning of "low quality" stems metaphorically from the notion that, that which is poor is somehow lacking something.