Plainly SEO is Search engine optimization which referes to varied strategies with the broad goal of bringing more people to your website the first way, by improving your search engine rankings. Social media optimization (SMO) on the other hand is just one part of SEO in as much as it contributes to how people find you online.
SEO can be used to target different kinds of searches, including image search, local search, video search, academic search, news search and industry-specific vertical search engines.
SMO is used to increase website traffic via social media which may include RSS feeds, social news and bookmarking sites, video and blogging sites, as well as social networking sites, such as Facebook, Twitter, Google+, Tumblr, Pinterest, Instagram, Vine, etc.
Plainly said SEO is the big picture of how you are discovered online while SMO only targets social media traffic