The specific purposes of social media and SEO are very different. Social media is essentially about branding and communicating with customers and potential customers while SEO is about increasing rankings in the search engines that lead to good quality traffic. The overall aim of both, though, is to increase business.
Social media does this by interacting with people and making them more aware of a brand, while SEO does it by improving the rankings for things that potential customers will search for when seeking products or services.
Via Antonino Militello