Well, you're having it both ways, eh? I'm right and wrong
Groups can belong to Groupings. A Grouping can hold as many groups as you want it to.
I've found that some activities will *only* have Groupings. For instance, an external link has no provision for groups, but can be set to work for a specific Grouping. To do this I make Group A and put it in Grouping A.
But Assignments will work with just groups. In the course settings, under "Groups," I choose separate groups in the drop down and Force group mode set to yes. All activities that work with groups then do not show each group's activities to each other. Students in Group A cannot see the submissions of other students in that group. But also, Group submission in the assignment is set to No.
Group submission is relatively new to Moodle, and I wish HQ had thought about the confusion two meanings of "groups" would cause.
And, if you really want to get psychedlic, try grokking "cohorts."