The difference is subtle, and to a certain extent depends upon your preference.   Clicking on a group (on the canvas) will select the all the objects in that group and they can then be moved / transformed as one. To select individual objects within the group you must Ctrl + Click or Double Click.   Objects nested in a Layer are still treated as individual objects, and can be selected directly on the canvas. So to move all of them at once you'd actually have to select the pare