We use much with singular uncountable nouns and many with plural nouns:
[talking about money]
I haven’t got much change. I’ve only got a ten euro note.
Are there many campsites near you?
Much and many are also more formal than a lot of.
Much and many are used in negative sentences, whereas a lot of is used in positive sentences.
I don’t have much money, but I have a lot of good friends.
Lots of functions similarly to a lot of, but is more informal.
From the Cambridge Dictionary. Click on the link to learn more.
Much, Many, A Lot of, and Lots Of