The way I would explain the difference is that a "dealer" is essentially someone who buys from and sells to the same "audience".
A merchant (as in a coal merchant) is a wholesaler is someone who buys in bulk from a supplier and sells them on to a [different] customer. Unlike a dealer, he would not (normally) sell the same type of goods back to his supplier.
An Antique dealer fits into the first category.
For further info see:
AskOxford: dealer &
Hope this helps