Members in a group can only belong to the same group membership level, and it is not possible for a member to belong to more than one level. Here is how the group level works: Each group pays the same membership fee (regardless of the size of the group) and everything else is exactly the same across all members (fields, renewal date etc.) . Since the group admin is probably paying for the whole group he/she pretty much has access to all the details about members he/she brings into the group. This means those who want to join an existing group cannot do so by themselves, only group / site admin can put new members into existing groups. However, anyone can start his/her own group by applying / switching to the group membership level, making it possible to create many different groups within the same group membership level. To leave the group a group member would have to switch to any other membership level.
Hope this clears things out, and let me know if you require further clarification.
Jim Sympathy, Fluid Apricot