Each shape has a shapesheet. Grouping two shapes will create a new shape that refers to (and controls) the other two shapes. You end up with the a shape with three shapesheets. The original shapesheets are left intact.
When you use any of the commands under the Operations menu, like Combine with two shapes, both shapes are combined into a single shape. So you will end up with a single shapesheet that will have multiple Geometry sections. Also the original Geometry sections will be altered depending on the operation.
Also Each shape can have a single colour, grouing will retain the original colours while Combining the new shape will take on the colour of the first shape selected.
John... Visio MVP