The difference lies in the accessibility. For discussions any messages posted here will be viewable by all members of the class. For the e-mail the messages are private going only to the members you have selected.
Can I remove a Discussion posting?
All postings on the discussion board are permanent postings, you will not be able to remove these postings once placed, so be careful NOT to post your assignments here by mistake. When you post your assignments to your instructor, check to make sure you are in E-Mail.