Is SEM different from SEO?

SEO is part of SEM.

SEM IMO consists of,
1. SEO
2. PPC
3. PFI ( Optional )
4. Link Building
5. Affiliate SE Marketing
6. ROI and conversion tracking
7. Sponsored Search engine listing(some search engines).
8. Shopping feeds ( shopping search engines )

SEO - Search Engine Optimization, Ability to improve a site to make it relevant to Search Engine Algorithm and make the algorithm rank a site based on User queries.