This is a tricky question: in definitional terms the words mean pretty much the same thing, and the differences are of nuance (or custom) only. I don't think you'll find an easy rule that will always tell you which one is best to use. Some random thoughts...
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AnonymousCould anybody tell me how to differentiate them when they are used as an noun?"in the dark" is the typical usage of dark as a noun. "afraid of the dark" is another. It tends to be less truly noun-like than darkness because it usually means "dark time(s)"
CalifJimIt seems to me that dark always occurs unmodified; only darkness can be modified.
I think that it can also be used to describe deep emotional turmoil as well.
"What could you possibly know of darkness like mine?" It can be used to describe guilt, loneliness, depression, hopelessness, a great loss.