Pay Per Click: (PPC) Advertisers bid on "keywords" that they believe their target market would type in the search bar when they are looking for their type of product or service. These ads are called "sponsored links" or "sponsored ads" and appear next to and sometimes above the natural or organic results on the page. The advertiser pays only when the user clicks on the ad.
Search engine optimization: (SEO) A subset of search engine marketing that seeks to improve the number and quality of visitors to a web site from "natural" search results. The quality of visitor traffic can be measured by how often a visitor using a specific keyword leads to a desired conversion action, such as making a purchase or requesting further information.
Search Engine Marketing: (SEM) A set of marketing methods to increase the visibility of a website in search engine results pages (SERPs). The three main methods of SEM are Search Engine Optimization, Pay Per Click Advertising, and Paid Inclusion.
Definitions courtesy of SearchEngineWatch.