I don't really think there is a difference. If there is one it's very small. Plenty is for when you have too much or enough of something. "I have plenty of food to take home." The word many is used to say there is alot of one thing. "There are many cats here." The word several would be used for about 3 to 5 things usually. "I had several dogs." (It makes sense here because most people dont have 6 dogs or more) Much is used to say the amount of something. It's usually used in a question. "How much does this cost?" "How much can you buy"?