How is the difference between “to cite” and “to quote” made clear in German?

Question

In English, there’s a difference between the verbs to cite and to quote (both links refer to Merriam-Webster).

The website differencebetween states (and I quote):

Cite vs Quote

The English words “cite” and “quote” are very similar and are used by people, sometimes, without knowing the differences between them. They cannot be interchanged or confused with each other. “Quoting” is basically repeating something someone has said or written verbatim, and “citing” means giving reference to a particular subject or words or thought by some person who is proficient to prove a point or theory or thought.
[…]
“Quoting” refers to reproducing the words of another person verbatim; “citing” refers to giving an example of some subject for substantiating oneself.

Google Translate offers zitieren for both to cite and to quote, and Leo lists zitieren and anführen (among other meanings) for both.

If I want to be precise and retain the meaning of quote or cite, how should the following sentences be worded in German?

1. The judge cited a number of laws to prove his point.
2. The student quoted Shakespeare in his presentation.

Answer 1

You are correct in assuming that the two meanings of cite and quote are often merged (and mixed up) in the one German word zitieren, much like the two English words are sometimes imprecisely interchanged.

The German term for using someone else’s words verbatim (word for word), i.e. the English quote, is zitieren (meaning 1 in the Duden entry).

In the following two sentences, zitieren means that a passage of text is quoted without alteration:

1. Ich zitiere [wortwörtlich] den Bericht der letzten Vollversammlung.
2. Um Goethe zu zitieren, „sag’s ihm, er kann mich im Arsche lecken!“

There are other ways to say this, depending on context. For example, in our second sentence, you could also use bemühen ironically:

Um Goethe zu bemühen, „sag’s ihm, er kann mich im Arsche lecken!“

The English verb to cite is a bit more difficult, because it may mean to quote, but it can also mean to just refer to something without actually quoting it. The German words anführen and verweisen correspond very well to this: They tell us that some text, opinion etc. is used. That actual piece of text may or may not be quoted (meaning 2 in the Duden entry of anführen; meaning 2 and 3 in the entry of verweisen):

anführen
2a. vorbringen, erwähnen, aufzählen
2b. benennen
2c. zitieren, wörtlich wiedergeben

verweisen
2. auf etwas hinweisen, aufmerksam machen
3a. veranlassen, sich an eine bestimmte andere Person oder Stelle zu wenden
3b. (Rechtssprache) übergeben, überweisen

To sum it up: If you quote something verbatim, always use the original wording, and call it zitieren / Zitat. If you cite something without quoting its words, like a reference to another work in your term paper, call it verweisen / Verweis.

And finally, using the examples from the question:

1. The judge cited a number of laws to prove his point.
   Der Richter führte eine Reihe von Gesetzen an, um seinen Standpunkt zu belegen.
   Or: Der Richter verwies auf eine Reihe von Gesetzen, …
   [He may or may not have additionally quoted them.]
2. The student quoted Shakespeare in his presentation.
   In seiner Präsentation zitierte der Student Shakespeare.
   [He actually used Shakespeare’s words.]

Answer 2

You can only quote someone, while you can cite someone or something.

German speakers don't make a difference, it's both either zitieren (to cite/to quote) or wiedergeben (to quote/to cite).

Jürgen gab bloß Thomas wieder.

Jürgen just quoted Thomas.

Jürgen gab bloß wieder, was auf dem Schild stand.

Jürgen just cited what was written on the sign.