Unfortunately in theoretical computer science no single group plays all these roles and thus one interacts with a large number of professional societies during an academic career. Let's look at some of them.
First most comes the Association for Computing Machinery (ACM) as the largest society devoted to computer issues. ACM tries to cover the entire computing profession so computer science research issues do not get center stage. They do publish several journals and give many of the important awards such as the Turing award.
ACM has a number of special interest groups (SIGs). SIGACT, the Special Interest Group on Algorithms and Computation Theory, is the main organization devoted to theoretical computer science in the US. They sponsor STOC and other conferences and publish SIGACT News. Many theorists join SIGACT without joining ACM.
The IEEE Computer Society also deals with computer issues and has a Technical Committee on Mathematical Foundations of Computer Science that sponsors conferences including FOCS and Computational Complexity. Why do we need both a Computer Society and ACM and a SIGACT and a TC-MFCS? Perhaps for the competition?
None of these societies serve as a strong advocate for computer science research and so we have the Computing Research Association. The CRA has as its members not individuals but academic departments and research labs. They have a newsletter, advocate and keep us informed on government policy on computer science, and collect information such as the Taulbee Surveys giving salary and job information in CS research. The CRA also has a strong focus on women's issues in CS research.
Let's not forget the Society for Industrial and Applied Mathematics (SIAM) that helps sponsor some conferences (SODA) and publishes the well-respected Journal on Computing.
The European Association for Theoretical Computer Science (EATCS) covers not just Europe but captures theory from an international perspective. They sponsor conferences like ICALP and publish a hefty bulletin three times a year. Also many countries have their own computer science and/or theoretical computer science societies.