If you're tired, you should get some rest. If you're tired of being tired, you might need to eat better and exercise more. If you're tired of being told what to do, you should stop asking for advice.
Tired can also mean that something is old news, or worn out to the point where people don't want to hear it anymore. Although you still find them funny, your co-workers think your impressions of your favorite cartoon characters are pretty tired.