For a light fixture, if I ground the wire to the light fixture and the wire in the box is also grounded, do I need to connect the two grounded wires? The cooper wire within the box is extremely short, making it very difficult to connect it to the cooper wire on the light fixture. Thanks
You do need a ground connection between the fixture, and the ground wire coming into that box (and to the box itself if it is metal).
If the incoming wire is too short and you only need to connect it to the fixture (not the box because the box is plastic), you can add an extension to the ground wire using an inline butt splice
Push the splice on the short wire and add an extra wire, often called a pigtail, to the other end of the splice. For a ground connection, the wire should be bare or green (assuming you are in the US)
If you need to connect the fixture, the incoming wire and the box (because the box is metal), you can use a conventional wire nut to join the short incoming wire, and two pigtails, one to the fixture and one to the box. You also can use push on connectors, like this one