Many people confuse these terms, and hopefully we can assist you in understanding this.
Payment Gateway is defined by WikiPedia as: A payment gateway facilitates the transfer of information between a payment portal (such as a website or IVR service) and the Front End Processor or acquiring bank. So this would mean that it is the system, that interacts with the website, and the credit card companies. Examples of payment gateways would be: Authorize.net, PSIgate, Linkpoint, Paypal etc.
Merchant Account is defined by Wikipedia as: A merchant account is a contract under which an acquiring bank extends a line of credit to a merchant, who wishes to accept payment card transactions of a particular card association brand. Without such a contract, one cannot accept payments by any of the major credit card brands. Examples of a merchant account would be: Your Local Bank, A dedicated Merchant Banking account.