In reality, there is a close affiliation between these two phenomenons. The major reasons are formulated as below. First, as we get tired, the tear duct will produce less fluid, which dries out your eyes. It stimulates the tear ducts when you rub your eyes, and spread moisture over your eyes. Second, tiredness also closes your eyes, so you may rub to keep them open. Finally, there's a connection between the muscles that move your eyes around and your heart. It also has effect on ocular muscles. While you are also putting pressure on your vagas nerve, it could reduce blood pressure, a reflex slows the heart. This might be relaxing if you feel very tired.
No, you can't rub your eyes to release the tiredness of your eyes. Because rubbing your eyes can turn red for rubbing your eyes. While you can use self-massage relieves tired eyes, because it can increase the circulation to the eye area. Also you can use some eye-drops to relieve your eye tiredness.
When you are tired, your eyes nerves will be loose too. Your eyes may not see things in the clear image. That is why you rub your eyes to see things clearly. However, rubbing eyes too much will cause the redness of the eyes. What's worse, the eyes may get infection because of the coming bacterium which is invisible. You could use the warm compress to release the symptom.