Hmmm....I'm a native English speaker and can't think of any difference. Every time I think of a sentence using one of the words, the other word would work just as well.

They're more or less interchangeable. They both mean the same thing, "every person," but "everybody" is slightly more informal and is used more often.

What's the *difference* between these two words: "everybody" and "everyone"? Hmm, good question. I can't think of an instance (at least off-hand) where I would use one exclusively instead of the other, so to me, they're interchangeable. For the following examples, I would tend to say it the first way, but I don't see anything wrong or awkward with saying it the second way. Everyone is entitled to his or her own opinion / Everybody is entitled to his or her own opinion. I inadvertently tweeted an invitation to a party, and everybody came. /… and everyone came. When the test proctor asked who needed more time to finish the test, everyone raised his hand / …everybody raised his hand.