Okay in a nutshell.
As a general rule
Changing or add groups to a member is done via the member manage section of the control panel.
But never uncheck the default user group.Just add the group or groups you want them to have.
FYI.
If you have subscriptions enabled they will be automatically added to the subscription group when they subscribe.
They will automatically be removed from the subscription group when they expire or cancel.
If you promote them via number of posts they will automatically be added to the group. via the control panel groups section
With that said yes you can also add them manually for any reason in the member manage group section
