"Businessman" is a general word for a man who works in any kind of business-- basically any kind of white-collar job. "Merchant" refers more specifically to someone who sells something, often one specific item or category of items, and often in a setting like a marketplace. "Dealer" refers to either a person or a company from whom/which customers can purchase a certain product. It is also the word we use to refer to people who sell things illegally-- for example, "drug dealer". And a trader is someone who trades one product for another product, instead of charging money for it. This is how I personally understand these words as a native speaker of American English. But it's possible that other native speakers might feel differently.

there's a trader too