in der German Language beta-Version von
German Language Stack Exchange [1] findet sich die folgenden Frage:

What’s the difference between “genau” and “stimmt”? When somebody agrees with a point made in conversation they often say "genau" or "stimmt" (often preceeded by "ja").
So what is the difference? Is one slang and the other standard? Or is one regional?
(I usually spend my time in Germany in Bavaria or Berlin but my friends in Berlin often moved there from some other region so I get it all mixed up in my head.)
word-choice usage regional slang interjections

Und daraufhin sind Antworten wie diese zu finden:

You can even say "ja, stimmt genau".

Yes, that’s exactly correct. Oh look, it works in English, too.

I sometimes teach foreigners the word "genau" and tell them that’s all they need to participate in a conversation with a German...

Yeah that will work well with a lot of people... good idea! :)

Ja genau, stimmt!

I personally use both words randomly to agree with what others say. Neither of these is rude or slang. In my opinion they can be used in a formal (business) discussion without any concerns.

Treffend bemerkt (just anaother related way to express my approval with the answer from Markus)

Nevertheless I think "stimmt" is more "you convinced me" while "genau" is "This is exactly what I thought all the time."

It depends on the context. If a waiter or a call center employee re-reads your orders to make sure the correct products are delivered, "stimmt" and "genau" can be used entirely interchangeably to confirm the correctness.

Both words are standard German, but I think "genau" is used more often in small talk. As Jan says in his comment, if you’re on the receiving end of a discission, it is quite sufficient to say "genau" at the appropriate points. To me, "stimmt" would sound less natural in this context (but that might indeed be a regional thing). For me, "stimmt" is connected with a little more thinking: If I agree without having to think, I say "genau" (or "ja, genau"), if I hesitate before agreeing, I say a little more thoughful "stimmt" (or "ja, stimmt").

I don’t know if there’s a regional difference, but for me it is genau the other way around. People here use "genau" to mean "exactly", while "stimmt" means any kind of affirmation, up to "still listening".

Actually it’s simple for speakers of English, because there are simple, yet precise translations available:

genau = exactly/precisely
stimmt = correct/true

The use cases in German may differ from the English language, but the meaning is very clear. Neither of them is an abbreviation of the other or a combination of both, as some comments state.

Something is either correct or not correct (for example “not entirely correct”). The expression stimmt genau does not mean, that something is even more correct than correct, because that’s not possible.

People use more than only one of the two in order to express their personal degree of approval (hopefully not to express a “degree of correctness”), or simply to answer in more than one word. In German short answers are common and we often have to learn, that simply saying no or yes often does not sound very friendly, although those can be correct answers.

Eine - wenn auch nicht repräsentative - Umfrage bei den "Native Speakers" kam heraus, dass das Wort "genau" eine zunehmend inflationäre Verwendung findet. Selbst bei Leuten, die, wenn sie zum Beispiel im Verlauf eines Vortrage einen Pause machen, zur Überbrückung derselben das Wort "genau" einwerfen, um den Eindruck der Kontinuität ihres Vortrages herzustellen.

Das Ergebnis der eingeholten Stimmen und Meinungen lässt sich vielleicht so am ehesten Zusammenfassen:

Das Wort "genau" habe sich im Verlauf seiner inflationären Verwendung in so etwas wie um ein "stimmt light" verwandelt, bei dem es nicht mehr primär um die Frage der Zustimmung oder Ablehnung ginge, sondern um eine eher "epathiestützende Massnahme" die vor allem dann zur Anwendung gebracht würde, wenn die Befürchtung bestünde, dass der aufgebaute Kommunikationkanal ohne einen solchen Einwurf zum Versiegen kommen könne.

Anders gesagt: Wenn das "stimmt" vor allem eine Zustimmung in der Sache signalisiert, ist die Funktion von "genau" eher eine Art der formlosen Zustimmungserklärung zur Förderung und Bekräftigung eines Dialoges.

"Stimmt"?