Any one means any single person or thing out of a group of people or things. For example:- I can recommend any one of the books from this site. Anyone means any person. It's always written as one word. For example:- Did anyone see that girl?

"anyone" appeared from fusion of "any" and "one" today "anyone" is an independent word which means "any person or any representative of a group" The two-word form "any one" is not the same as the one-word form "anyone" and the two forms cannot be used interchangeably. "Any one" means ‘any single (person or thing)’, as in: not more than twelve new members are admitted in any one year "anything" refers to a thing, no matter what (except living things) "any thing" is rarely used and may refer to a particular "thing" E.g. have you seen any of these things? "thing" here may be anything which is allowed by the semantics of the word "thing"