Union is a boolean operation and combine is not. If it takes a few years to wrap your mind around geometric boolean operations you are not alone. Be warned simplifications abound in the following, but based on the question I think it is a good place to start.
Union takes two shapes and combines them into one shape. Combine takes two shapes and treats them as a single shape while retaining the two shapes. Group, under the object menu, takes two shapes and makes sure they are all moved around at once. So, when do you use them?
You use Union when you want to make a single shape. If you take two squares you can make a complex shape by unioning them. If you combine them, the glowforge will cut the insides and outsides of the shape. Union just gives you the outside.
So why use Combine? When you use the Edit Paths by Node tool in Inkscape it will only work on one shape at a time. If you combine two shapes you use that tool to manually edit nodes, and combine them, with that tool.
So what about Group? Group is very useful for organizing. The more stuff in your file, the more it needs organizing. It is very easy to grab twenty objects and move them, but ooops, you didn’t grab the twenty-first object and now everything is RUINED!!! Edit-Undo, Edit-Undo, Edit-Undo…
To me the biggest difference between Group and Combine is with Group you can have a black square, a blue circle and a green star. Combine also combines colors into one. As colors are important for ordering cut operations in the GFUI, Group is important.
In the illustration below, the top two squares are independent. You can grab each one separately. The middle two squares are Combined and are treated as one (as seen by the dotted lines). The bottom two squares were unioned and are now one object.