The group ensures that any member of that group can connect to the server. Typically groups will then be used to grant access into the database. However, it doesn't have to be this way. In the situation you described, an individual user, who is a member of the group, was granted access. This is permissible in SQL Server. The key is think of the login as access into the SQL Server. Once their in, any individual user or group of users can be granted access into specific databases.
K. Brian Kelley
@kbriankelley