I think they are just two different notations of the same thing.
The Wikipaedia page of quotation says the same:
A quotation or quote is the repetition of one expression as part of another one, ...
Some people just used the first and others the second form and once both tags existed they popped up automatically when someone write quo...
in the Tags field. Most people don't know the difference as well so they tag their questions with both, just to be sure.
I would say they should be merged, e.g. quote as synonym of quotation.
And punctuation should be enough. Questions about quotation-marks can simply be tagging with both quotation and punctuation.