quote are names of LaTeX enironments. They are different, though closely related. Nevertheless, I don't think it's worth to distinguish. Though I would not pick one and convert to other one into a synonym.
I suggest we use the concept tag quoting similar to our other concept tags compiling, installing etc. and convert quote and quotation into synonyms of quoting, which now covers further quoting environments and packages. Also by this, we would merge, so questions with both tags would keep only quoting.
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.