The two word families "quote", "to quote" and "citation", "to cite" seem to be synonyms to me as a German native speaker, if we look at their meaning to reproduce information somebody else published.
Are they really? Or is there a slight difference in their meaning? If yes, when would I use one and when should I chose the other?
Update:
As the problem I have seems to be unclear for people who don't speak German: In German we only have one word for both of them! We say "zitieren" if we say/write/… something that was originally published by someone else and reproduce it word by word, as well as with giving a reference. From what I already learned, those two aspects are the main differences, but my language does not make any difference here. I hope this helps you to understand that it is not really possible for a German native speaker to easily distinguish those two words with a simple dictionary.
Best Answer
The meanings can overlap.
To "quote" is to repeat someone else's words, in a way that indicates that you are repeating someone else's words, as opposed to incorporating them into your own work without any explicit identification that they are copied. (This could be plagiarism or it could be an allusion, but that's a different issue.)
To "cite" is to reference some other work. You may be quoting it word-for-word or you may simply be referring to it. "Cite" can be used to mean "quote", but it would rarely be used if you gave a quote without a reference, and it can be used when you give a reference without a quote.
Examples: "As Winston Churchill said, 'I have nothing to offer but blood, toil, tears, and sweat.'" This is unquestionably a quote. It might be called a citation.
"According to Barclay's Famous Quotations, Winston Churchill once said, 'I have nothing to offer but blood, toil, tears, and sweat." This is both a quote and a citation.
"In his History of Britain, Charles Stover says that Churchill called on the British people to be willing to make sacrifices." This is a citation but not a quote. It is not a quote because we are not repeating any exact words.
And to be complete: If I wrote a novel, and at some point in the novel I write, "General Framnitz urged his soldiers to fight on. 'I have nothing to offer but blood, toil, tears, and the billions of dollars of loot that we will get when we take the city'", that would be an allusion and not a quote, because I am not making any clear reference to Mr Churchill, and because I'm adapting the quote for my own purposes.
A citation can be informal like my examples here, "As he said in ...", or it could be a more formal reference, like "See Stover, Charles. History of Britain. Fwacbar Publishing, 1964, pp 85-86" (The exact formatting varying depending on what style guide you're using, if any.)