A notary is a state licensed individual to verify signatures, you would have to check the law in the state or country where the signature is being notarized or the doucment is being used for legal purposes.
No, it is not the same thing, as a notary is an individual certified by the state to perform notarial duties.
Some states are looking to allow notaries to use digital or electronic signatures to notarize digital documents, but as a previous poster stated, this varies by state.
In any case, just putting a digital signature on your document will NOT notarize it, though it may prove time and authorship, based on how you acquired the certificate to sign the document in the first place.
I should correct my statement about notaries, they are individuals either licensed or authorized by law to administer oaths and statutory declarations, witness signatures, certify documents, and certain other acts as authorized by the jurisdiction that authorizes the notary. It should be noted that certain government offices can act as notaries under prescribed circumstances. The U.S. Internal Revenue Service allows certain accepted individuals to attest to the authenticity of copies of certain documents in lieu of a notarized copy of the document.
With the advent of public certificates for electronic signature, some state or countries may allow the verifiable certified electronic signature in lieu of a notarized signature under very strict requirements for the public certificate for the signature, but this will depend on the local law applying to the type of document or action and there is no blanket rule that covers electronic signatures as replacing the physical signing and notarizing of the signature of documents.
If you are planning on trying this, consult an attorney and state officials in the jurisdiction were you will doing this or the documents will be filed in to make sure you are meeting all the requirements for the certified electronic signature.
George Kaiser