What is the difference between Digital Marketing and Social Media Marketing?

Social media is simply a subset of digital marketing and is about the use of social media sites for marketing.
In social media, a marketer relies on facebook, twitter, foursquare and email, all of which happen to also be internet based marketing tools.
Digital marketing uses all digital channels available to communicate with the target client/audience.
This stresses the fact that no print media is used.
Included in digital marketing is Social media, Mobile marketing, SEO, QR codes, E-mail marketing etc.
This form of marketing provides a large platform for analyzing the behavior of the target client and to understand how to better target them in the future.

Social media is just one component of digital marketing.
Social media and SEO specialists are fine and good, but at the end of the day they can’t be relied on to drive meaningful results.
A multichannel approach in digital produces better results, and firms that can specialize in owning the right mix of those channels have a better value proposition than “pure play” specialists.
Tactics such as the development of a keyword universe, search engine optimization (SEO), e-newsletters or what a recent seminar attendee interestingly called "digital direct mail", websites, blogs, local marketing including Google's Local Place Pages, AdWords, banners, and other methods of paid online advertising, and even review sites all fall under the heading of "digital marketing".

--------The brief answer is Social media is just one component of digital marketing.Digital Marketing is an umbrella term that covers almost everything related to digital.-----------

Social marketing is a sub category of digital marketing whereas digital marketing involves all online marketing such SEO SEM ppc campaigns

An easy way to think about the difference between these marketing strategies is the difference between marketing tactics and marketing strategy. On a larger canvas social media marketing is a part of digital marketing. 

In-short, Social is a subset of (digital) marketing.