Timoteo is mostly right.
A merchant buys and sells goods, but this term is a little old-fashioned.
An entrepreneur is a businessman/woman who has taken initiative to start their own business, or has given new ideas to an existing business and reshaped how a company works. Entrepreneurs are proactive people who take risks in business. (Not always the same as a businessman)
A businessman is a very generic term for anyone who works in the corporate world. If you are confused on what to call someone, use businessman (or businesswoman!)