Types of Notarizations
Whether you are a Notary Public or not, you can benefit from knowing the difference between the most common Notarial acts. Typically, a document that needs to be Notarized will already have the default language indicating the type of Notarization. However, if it does not, a Notary Public cannot choose what type of Notarial act should be performed for you. This is why it is good to at least know the basics about common Notarizations.
Common Notarizations:

The first most common Notarial act is an Acknowledgement. An Acknowledgement is usually identified by the wording: "On ______ before me, ____________ personally appeared _________". This is used when a document does not need to be signed in the presence of a Notary. The Notary must verify that you are in fact the person who signed (you Acknowledge that you signed) the document AND that you voluntarily signed the document. It is common practice to sign the document in front of a Notary at the time of the notarization, but it is not necessary. The main purpose of an Acknowledgement is for the signer to "Acknowledge" or affirm that they in fact singed the document and for the Notary to confirm the identity of the signer.
Types of documents that may use an Acknowledgement could be Deeds, Mortgages, Deeds of Trust, or other documents pertaining to valuable assets.

The second most common Notarial act is a Jurat. A Jurat is identified by the wording: "Subscribed and sworn to (or affirmed) before me on this ______ day". The main difference between an Acknowledgement and a Jurat is that a Jurat requires an Oath or Affirmation from the signer stating that the contents of the document are true. The Notary is also required to verify the singers identity.
For a Jurat, it IS required for the signer to sign the document in the presence of a Notary, after they have sworn to, or affirmed, that the contents of the document are true.
Types of documents that may use a Jurat are Wills, Trusts, Deeds of Trust, or other documents.
Other Notarial Acts:

A copy certification confirms that a reproduction of an original document is a full, true, and accurate transcription or reproduction of the original. Common documents that get requested to be certified are Marriage Certificates, Birth Certificates, Vital Records, and so on.
In California a Notary Public may only certify copies of Power of Attorney, or the Notary’s journal, if requested by state officials or a court of law.

Oaths or Affirmations can be administered separate from a Jurat, affidavit, or other document. The purpose of administering a verbal oath or affirmation is to compel a signer to truthfulness.
An oath is a solemn pledge to a Supreme Being. An affirmation is a solemn pledge on the individual's personal honor. Again, the choice should be made by the signer.
Non-Notarial acts:
In California, a Notary Public is not authorized to witness a signature as part as their notarial duties. A document that needs to be witness should state "Signed (or attested) before me…”. A Notary may witness a signature, but not charge a fee or record it in their Journal.
Lastly, remember that these acts are not for the Notary to decide. If you are ever unsure about what type of Notarization that is needed, you should contact the authority who issued the document, or an attorney.