Many is for countable things. Much is for uncountable amounts. Many passages. Much time. Same count-versus-mass test as fewer versus less.
How the pair sits
How many questions did you miss? You can number them. How much time is left? You measure it. Much students and many water are both wrong. In questions, many often pairs with a plural noun. Much often pairs with a mass noun or with too and so: too much noise.
Amount versus number is the noun version of this split, in amount versus number. The bigger comparison set is in comparison words. Word-choice traps overall are in word choice.
The bottom line
Countable: many. Uncountable: much.
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