Interchangeable in meaning — both mean any person at all, and both are singular. Anyone is a little more formal and commoner in writing; anybody is more conversational. The distinction worth knowing is anyone versus any one, two words, which means any single item of a set.
The core difference
None in sense. As with someone/somebody and everyone/everybody, the pair differs only in register: anyone leans formal and written, anybody leans spoken.
Where they appear
Both are commonest in questions, negatives and conditionals, which is where the word any naturally lives:
- Did anyone call? — question
- I did not tell anybody. — negative
- If anyone asks, say nothing. — conditional
In a plain positive statement, anyone shifts meaning to "it does not matter who": "Anyone can learn this" means every person is capable, not that one unspecified person is.
The distinction that matters: any one
Spaced, any one means any single member of a group, and it can refer to things as well as people: "Choose any one of the three." Closed up, anyone refers only to people. If you can insert "single" without breaking the sentence — "any single one of the three" — you want two words.
The grammar
Both take a singular verb — "Is anyone home?" — and both take singular they when referred back to: "If anyone calls, tell them I am out."
Frequently asked questions
Is anyone or anybody more formal?
Anyone is slightly more formal and commoner in edited writing. Anybody is more conversational. Neither is incorrect.
What is the difference between anyone and any one?
Anyone refers to any person. Any one, spaced, means any single item of a set and can refer to things: "any one of the options". If "single" fits between the words, use two.
Is it "anyone is" or "anyone are"?
Anyone is. The word is grammatically singular despite referring to people in general.