They mean the same thing and are interchangeable — both refer to every person in a group and both take a singular verb. The only real difference is register: everyone is slightly more formal and appears more often in writing, everybody sounds more conversational. Neither is more correct.
The core difference
There isn't a difference in meaning, and no rule requires one over the other. Style guides that once claimed everyone was more precise have quietly dropped the claim, because usage never supported it.
What actually separates them
Everyone carries a marginally more formal tone and is the commoner choice in edited prose. Everybody is the commoner choice in speech and in writing that wants to sound like speech. In a contract you would expect everyone; in dialogue you would expect everybody.
The one rule that does matter
Both are grammatically singular, so both take a singular verb:
- Everyone is here. — not "everyone are"
- Everybody knows the answer. — not "everybody know"
This trips people up because the meaning is plural — many people — while the grammar is singular. The verb follows the grammar.
The pronoun that follows
Referring back to either word has been awkward in English for centuries, because a singular word describes a group of mixed people. They is the long-standing solution and has been used this way since the 1300s: "Everyone brought their own lunch." That is standard, and it is far less clumsy than "his or her" repeated across a paragraph.
Every one, two words
Watch the space. Every one as two words means each individual item, and it usually points at something already named: "She read every one of the reports." That is a different construction from everyone, which only ever refers to people.
Frequently asked questions
Is everyone or everybody more correct?
Neither. They are interchangeable in meaning. Everyone is slightly more formal and commoner in writing; everybody is more conversational.
Is it "everyone is" or "everyone are"?
Everyone is. Both words are grammatically singular even though the meaning is plural, so the verb stays singular.
Can I write "everyone brought their own"?
Yes. Singular they has been standard English since the 1300s and is the natural way to refer back to everyone without the clumsiness of "his or her".
What about "every one" as two words?
Every one, spaced, means each individual item of something already mentioned: "every one of the tickets". Everyone, closed up, refers only to people.