Sounds like just typical struggle with learning terms from a new software. You're looking for Parenting in blender it sounds like, much like the grouping you're talking about.

How to do what you wanted:

Shift-A Cube Shift-A Cube G to move second cube(assuming you don't want them stacked) Shift right click to select other cube Ctrl+P select Object to parent one to the other(you would use Keep Transform if you wanted to keep them together but move/scale/rotate separate)

Look in the Scene graph on the right, they're still separate objects so you can assign different materials to their faces, unwrap, un-parent them with Alt+P, whatever.

If you wanted to merge the geometry, you'd use Ctrl+J to join them.