To paraphrase Abraham Lincoln, notarizations aren't always all one thing or all the other. Sometimes a notarization is both an acknowledgment and a jurat. And that's called a hybrid certificate.
In this case, the notarial certificate may combine both acknowledgment and jurat wording, meaning the signer must both acknowledge a signature and be administered an oath by the Notary. For example, your signer might be a partner in a business who is signing a contract on behalf of the partnership. His signature would need to be acknowledged and he also would have to execute a sworn or affirmed statement that he is a partner in the business. In this case, the notarial certificate may include the phrases "acknowledged before me" and "subscribed and sworn to."
In your journal you can describe a hybrid as an "acknowledgment/jurat"or "acknowledgment with oath," or something similar.
California Notaries cannot complete this type of hybrid wording, but, instead, must replace it with two separate certificates: an all-purpose acknowledgment and a jurat. That's because the state prescribes the exact wording to be used in each.