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.
Which of the two to use when? – I think it’s a matter of personal preference. I seem to use genau more often than stimmt.
There is also the lesser used exakt, which translates to exactly, if that’s better for you to memorize.