By the definitions there is not much difference. It's mostly in usage where they are different. Much is commonly used in the negative, example. "I don't have much time left." "I have much time left." sounds strange. "I have lots of time left." sounds correct. You wouldn't say. "I have many time left." You could say. "I have many hours/days left."
I hope the above is helpful. I hadn't thought about this until now. I now realize it can be very confusing.
@miguelc899 much, lots and many all mean the same thing. A big number of something. How and when they are used is very different. I'm not sure I can explain it well, beyond the examples I have already given. The best advice I can give you on usage is this. If you get your choice of words wrong. Your meaning will mostly likely be understood. You will get corrected and learn proper usage from there. I simply don't have the skills to explain the difference in a way you would understand.
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