Search engine optimization (SEO) is the idea of how important search engines like Google and Yahoo deem your website. Companies like Samsung would use SEO to show up on page 1 for the search "What laptop should I buy?".
Online reputation management (ORM) is the idea of controlling what people see when they search for you. For example, a customer has already decided he might want to buy a laptop from Samsung, the customer then Google searches "Samsung laptop reviews". Samsung would use ORM to have the best articles about the company displayed on page 1, and any negative articles on page 10+.