The purpose of an Acknowledgment is to ensure that the signer of a document is who they claim to be and has voluntarily signed the document.
To perform an Acknowledgment, the signer must personally appear before the Notary Public at the time of notarization to be positively identified and to declare — acknowledge — that the signature on the document is their own and that they signed willingly.
While it is common practice for the signer to sign the document in front of the Notary Public at the time of the notarization, it is not necessary. The signer may sign the document before bringing it to the Notary Public and declare, acknowledge, to the Notary Public that the signature on the document is theirs.

Acknowledgments often are needed for documents concerning valuable assets, such as deeds, mortgages, and deeds of trust.

The purpose of a Jurat is for a signer to swear or affirm that the contents of a document are true. Depending on the jurisdiction, it also can be known as an affidavit or a verification on oath or affirmation.
For a Jurat, the signer must personally appear before the Notary Public and sign the document in their presence. The Notary Public must then administer an Oath or Affirmation and have the signer speak aloud his or her promise that the statements in the document are true. The choice between an Oath or Affirmation should be made by the signer.
Administering the Oath or Affirmation is a vital part of performing a Jurat or verification because the signer is affirming that the contents of the document are true, and he or she may be prosecuted for perjury if the contents are not true. 

California requires a signer to provide proof of identity for a Jurat.

In some cases, a signer may simply need a Notary Public to administer an Oath or Affirmation orally, rather than as part of a Jurat​, affidavit or other written document. The purpose of administering a verbal oath or affirmation is, again, to compel the 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. 

The choice between an Oath or Affirmation should be made by the signer.

A Copy Certification confirms that a reproduction of an original document is a full, true, and accurate transcription or reproduction of the original.
To perform a Copy Certification, the person in possession of an original document (known also as the "document custodian") takes the original document to a Notary Public. The Notary Public typically will make a photocopy of the document and complete a Certificate for the Copy Certification to confirm that the photocopy is a true, accurate, and complete copy of the original.

Note: It should be clarified that the State of California limits this type of Certification and authorizes only and exclusively the certification of Original Powers of Attorney and Journal entries.

Certified copies of Journal entries are issued if requested by the Secretary of State, Court Order and Subpoena, and are not available to the public. However, the public may request a simple copy of Journal Entries.

To request a simple copy of any Journal entry, the interested individual must submit to the Notary Public a written request that includes:

WHO: Name of the parties.

WHAT: Document Name/Type.

WHEN: Month and Year of Notarization.

The subscribing-witness certificate is typically used when a Principal Signer who cannot appear before the Notary directs a third party (the Subscribing Witness) to witness that Principal’s signing or acknowledging of a document and then to bring the signed document to the Notary Public to vouch for its execution. 

This Subscribing Witness signs (subscribes) on the same document and takes an Oath or Affirmation, pledging truthfulness, from the Notary Public. The witness should be personally known by the Notary Public and identified by a Credible Witness whom the Notary Public personally knows. 

In most states, a Proof of Execution by a Subscribing Witness is a legally acceptable substitute for an Acknowledgment by the Principal Signer. It is never an acceptable substitute for a Jurat, which requires the Principal Signer to sign and take an oath in the Notary Public’s presence.