...and Prayer fits in each type!

Group Type=Group Activity

Small groups are often defined by their main activity. This is a good approach, but let me offer my alternative.

Before deciding on a specific activity for your group, think through the central reason for which the group exists.

Process-oriented groups focus on the spiritual and/or social relationships among the members. What the group does is secondary.
Content-oriented groups meet to study or discuss a biblical passage or topic. Little time is spent dealing with group dynamics.
Task-oriented groups meet to accomplish a purpose. The reason for meeting is why the group exists.
Need-oriented groups, sometimes called support groups, offer common understanding and encouragement.

Determining the primary focus of your group will help you decide on the specific activities your group should undertake.