When it comes to payment gateway options, there are plenty to choose from.  One of the original companies whom I worked with offered both a merchant account and a payment gateway – wasAuthorize.net.  The newer options include Stripe where they offer a flexible integration solution, loaded with features like monthly billing, coupon options, trials and unlimited subscription options.

A payment gateway is an e-commerce application service provider service that authorizes payments for e-businesses, online retailers, bricks and clicks, or traditional brick and mortar. It is the equivalent of a physical point of sale terminal located in most retail outlets. Payment gateways protect credit card details by encrypting sensitive information, such as credit card numbers, to ensure that information is passed securely between the customer and the merchant and also between merchant and the payment processor. – Wikipedia

A merchant account is a bank account that enables your business to accept card payments. You must have a merchant account in order to be able to accept credit cards. Most companies bundle the two services (payment gateway and merchant account) together but they can also be bought separately.