Shame is a much stronger emotion than embarrassment. To be ashamed about something or shamed by someone can affect you for all your life. To be embarrassed is usually just a momentary emotion. I am ashamed that I was so mean to her. I am embarrassed that I wore jeans to a formal dance.

They are completely different emotions. If you feel ashamed you feel guilty about something wrong which you have done. You lie, you steal, you cheat , you let your friends down. These are all things which you regret and feel ashamed of doing. Being embarrassed is simply feeling uncomfortable or awkward in front of other people. You say something stupid, people look at you and your face goes red. This is very different from feeling ashamed.