These words are interchangeable in their meaning of "every person," although everyone is considered by some speakers as more refined and euphonious than everybody. Both pronouns, when used as subjects, require singular verbs; accompanying pronouns should also be singular: "Everyone has (not have) an obligation to cast his (not their) vote." Spelled as one word, everyone means "everybody." Every one (two words) refers to each person of a group and is followed by of: "Every one of them is loafing on the job."
Dictionary of problem words and expressions. Harry Shaw. 1975.