The two Submit buttons do the same thing: in this case, they issue the download link and send a thank-you email to the recipient with a link to their thank-you/download page. We put a Submit button at the top and bottom of the screen to make them easy for users to find and less likely to be overlooked.
Hitting the Enter key also does the same thing as clicking Submit, so maybe that's what you were doing when typing the recipient's email address sent the link? You can hit the Tab key to jump from one field to the next (standard behavior with most online forms), or of course just use your mouse to click in each field you want to enter anything into before you hit Submit to issue the link and send the email.