Many English teachers argue about this. In usage, you can interchange them and nobody will call it an error. If they do say something, you wouldn't want to know them anyway. Consider them to be the same. If you like to worry, though, the people who argue about it say that there is a difference. Everybody - all the people in this group are treated as a single thing. "Everybody gasped." = All the people in this group gasped at once. Everyone - we are talking about a group of people, but with each person considered individually. "Everyone looked at his or her watch."

From what I see, the only difference between these two words are spelling and pronunciation, this case also applies to anybody/anyone, somebody/someone. Normally, I choose words with "one" before that with "body", which I even can't explain, maybe it's just my habit.