Maybe I can help clarify…
If you use the “Group” tool to add objects (any point or curve is considered an object), this creates a “visibilty” group, where you can show/hide a group from displaying in a draft block. In a sense it analogous to putting objects on a certain layer that can be turned on or off.
When using the Mirror / Rotate / Move operation tools you again select objects to add to a “source group” , and based on the attribute settings for that tool , a resulting “destination group” will be created.
That’s why I prefer to refer to group items, source items, or destination items, and it’s clearer what “group” one is referring to.
And like Grace said, currently you can’t add / delete objects from any of the groups - this is something will change. I’ve worked out add / deleting from a Group tool, so that will happen in the near future… with the operations tools to follow at some point.