"Wise guy" is slang. It refers to someone who thinks they know everything. The truth is nobody can know everything, so people who act like they do are referred to as "wise guy". It's derogatory. Wise man isn't really an expression in my opinion. To call someone wise is a compliment. They are smart but they aren't boastful.

PS. It can also mean that someone is getting 'too big for their boots'.

The previous answers are right. Sometimes English does go like this. Think about it: Why is it that when the alarm goes off, we have to turn it off??

Really???))) I would like to know it too :)

Wise man is a simple statement of fact, and is a little formal - it would be unusual to encounter in conversation. Wise guy is American idiom, and is essentially sarcasm, where the phrase is said to imply someone is the opposite of wise, or stupid. I believe it is probably a bit outdated now but perhaps an American can confirm this.