East Germany was ruled by the Socialist Unity Party (abbr. SED). They used the term socialism more often than communism. Here’s a good link
http://www.wisegeek.com/what-is-the-difference-between-socialism-and-communism.htm
“Socialism and communism are ideological doctrines that have many similarities as well as many differences. It is difficult to discern the true differences between socialism and communism, as various societies have tried different types of both systems in myriad forms, and many ideologues with different agendas have defined both systems in biased terms. Some general points distinguishing the two concepts, however, can still be identified.
One point that is frequently raised to distinguish socialism from communism is that socialism generally refers to an economic system, while communism generally refers to both an economic and a political system. As an economic system, socialism seeks to manage the economy through deliberate and collective social control. Communism, however, seeks to manage both the economy and the society by ensuring that property is owned collectively, and that control over the distribution of property is centralized in order to achieve both classlessness and statelessness.”