Digital marketing covers multiple touch-points such as paid ads and email, while social media focuses specifically on marketing to followers and potential followers through social media platforms. Social media is a form of marketing under the digital marketing umbrella.
With social media marketing you can communicate with your consumer base in a more casual, conversational, and immediate way than say through an email or blog post (depending on your brands tone of voice of course). It also encompasses its own wide range of skills and strategies, from community building to engagement-driving copy (perhaps even creating a viral Tweet or two!).