This tag should be used for questions about someone's words and its context, reasons, origin, authenticity or purpose. It can also be used for the motives behind use of somebody's words by somebody else, e.g. "why did Smith quote Jones?"
The quotes tag should be used if you are referring to someone's words. You may ask of the context of the saying, reasons or purposes of a particular sentence. It can also be used in relation of use of somebody's words by somebody else, eg. "why did Smith quoted Jones?"
A paraphrase is a sentence related to the original having the same meaning, but using different words. A parody is a paraphrase that is intended to look like the original sentence, having the original structure, but humorous meaning (sometimes different than the original) by changing some words. Both are usually understood only if the previous (original) sentence is known, and both can be considered as quotes.
A related sentence, like a parody, but having no humorous aspect, could also be considered as a quote. For example Polish king John III Sobieski after the winning in Vienna in 1683 sent to the pope a letter with Latin words veni, vidi, Deus vincit which was strictly related to words of Julius Caesar veni, vidi, vici.