In a vector environment, it's useful to understand the difference between Combining a group of selected objects and Grouping them, especially when it comes to applying fills to either one.
Combining objects allows us to make compound objects. The classic compound object is the donut hole effect. If a white circle is placed over an already existing and larger black rectangle sitting on an even larger red rectangle, then you’ll end up with a white circle on top of a black rectangle sitting on a red rectangle. (Image 1) If, however, the white circle and the black rectangle are both selected, going to Arrange/Combine will create a compound object and the interior of the circle will become transparent like a donut hole and the red of the largest rectangle will show through that donut hole.
Compound shapes are more dynamic and the donut hole effect is a good example of that. Another example is what happens when compound shapes are filled. To demonstrate this, use the Artistic Text tool and just type a capital ABC. Make it large enough to see clearly and with it still selected, go to Arrange/Break Artistic Text Apart. The letters will no longer function as type, but instead as ungrouped shapes. Letters like the A and the B will each already be Combined with the trapped space inside each letter being transparent (donut hole effect).
If all three letters are selected, they can be Grouped or Combined even though the A and B are already compound shapes. If they are selected or even Grouped and a Fountain Fill is applied, then each letter will show the full transition of the gradient color within each letter. (Image 2) If, on the other hand the letters are selected and Combined (Arrange/Combine), then the Fountain Fill will be applied as if the three letters were a single shape. That means that the color gradient would travel across all three letters, creating a very different effect. (Image 3)