SEO is a subset of SEM,SEO is a method by which SEM is accomplished.
SEO is a way to improve over time, the relevency of the ads that appear with the search results, to the term or terms that were searched on.
Short for search engine marketing, SEM is used to describe acts relating to research, submissions and ranking a Web site within search engines to achieve maximum exposure of your Web site.
SEM includes things such as SEO, paid listing services and other search-engine related services that increases traffic to your Web site with more exposure.