SEO = the organization and curation (ie optimization) if your online content. You're basically helping search engines find your stuff, and in the method it wants.
SEM = marketing, but using the tools afforded to you by the search engines. SEO and SEM really do not overlap, and have entirely different uses. SEM is a subset of a larger marketing plan (assuming you have one, which sadly many do not). It may play off SEO'd content, or might go in another direction entirely like paid search (aka Google AdWords) that entirely ignores your SEO activities.
Got it?
I see a lot of really bad definitions for what SEO and SEM is. Too many "expert" bloggers have little knowledge in the real world of marketing.