SEO is used for making your web pages as “attractive” as possible to the search engines by optimizing various elements of each web page.
SEM stands for "search engine marketing" and
SEO stands for "search engine optimization."
SEM is the all-encompassing broad phrase that includes
SEO as well as paid search activities such as Google AdWords purchases.
SEO, simply a subset of SEM.
Search Engine Marketing is the process of researching and positioning a web site within search engines to achieve maximum exposure.
A SEM campaign includes
SEO, paid inclusion, pay-per-click, and other related services that will increase qualified traffic to your web site.
In a simple form,
SEO is what you do to your site and SEM is what you do outside of your site.