SEM is a broad term. It's everything that can be done to utilize the technology of search engines with the goal of promoting a web site and increasing its traffic, its "stickiness," and, in the case of sites that promote a business (or are a business), increase profits. SEO, therefore, would be a subset of SEM.
No SEM campaign is complete without SEO. Moreover, since the purpose of SEO is to make the site better for both search engines and users, you may find that it will suffice on its own. In any case, the advantages of SEO over the other aspects of SEM make it clear that, even if you are going to spend additional money on advertising and paid placement, SEO must be your first step in promoting your site.