Recovery is the process of overcoming a particular life problem such as alcoholism, drug addiction, gambling, childhood abuse, grief, etc., through inner change and personal growth, usually through some self-help program or psychotherapy. For many people this means specifically the 12 Steps. For others it means finding a group of people that share a common struggle.
A self-help group is a group whose members share a common problem and who meet together on a regular basis to help each other overcome it. The term "self-help" originally meant that they are not using professional help. Some prefer the term "mutual-help" because the members help each other, but others counter that self-help refers not to the group interaction but to the principles and methods learned from others in the meetings that the individual members apply to themselves.
Self-help groups are often referred to synonymously with support groups, but some make the distinction that support groups more commonly deal with sharing information about common problems such as chronic physical disease and grief, while self-help groups have specific programs of change and personal growth, usually in regards to addictions and other personal issues. This distinction, if one can be made at all, is not always clear, however, and there is a lot of overlap.
A 12 Step group is any self-help group which uses some version of the 12 Steps of AA. The 12 Steps are also used by many treatment centers and rehabilitation programs. However, most are not usually considered 12-step groups unless they also hold self-help meetings and follow some version of AA's Twelve Traditions.
The 12 Steps were written by Bill Wilson, co-founder of Alcoholics Anonymous, to summarize AA's program of recovery. They have since been adapted by literally hundreds of other groups to help an endless variety of problems. A complete listing is available on the AA Web Page. Detailed instructions for following the 12 Steps can be found in the book Alcoholics Anonymous, commonly known as "The Big Book". Some other 12-step groups have printed their own literature and word the Steps slightly differently.
The original reason for anonymity was to protect the members from stigma. Later, it was extended to protect the group from self-appointed spokesmen. When what is now Alcoholics Anonymous published their basic text, now known as "The Big Book", they listed the authors as "Alcoholics Anonymous". This became the title of the book, and then the group itself. Later 12-step groups imitated the name, as well as the practices. Members are requested not to identify themselves as such on TV, radio, press or film.