Notaries public serve two separate functions when notarizing documents. One is to provide verification that the maker of a document has signed it under oath, certifying it as true.
Another is to provide verification that a specific person signed a document freely and voluntarily. This is called an acknowledgement. The Notary will sign a statement that says something like, “X, who is personally known to me or provided satisfactory proof of his identity, signed (or acknowledged his signature on) this document and declared it to be his free and voluntary act and deed for the purposes therein mentioned.” The acknowledgement confirms the identity of the signer and the voluntariness of the action of signing, but the signer is not under oath and is not swearing to anything.