Answer by Ben posted to Stackoverflow (http://stackoverflow.com/questions/14971830/what-is-the-difference-between-e-signature-and-digital-signature/15050512#15050512), reproduced below.
“An eSignature refers to the electronic signing process that creates a legally binding agreement, while a digital signature tends to mean the cryptographic signature produced by public/private key signing.
A public/private key digital signature could be one of the signing methods used for eSignature.
The reason a digital signature is not an eSignature is that applying it alone won’t create a legally binding agreement, for example, you could apply a digital signature to secure some data for transmission through an untrusted network (in fact this was the original purpose of the public/private key).
By analogy you could think of your handwritten signature equivalent - you can sign your name on a blank piece of paper or a guest book as many times as you like, no legal obligation is being created upon you. It’s not only the signing method that creates a signature but the wider context.
I don’t think there is a strict answer to the authentication process for an eSignature. It may be better to look at it as a set of principles that need to be established, since this can spawn any number of specific processes. (By ‘authentication process’ i take it you mean the process to generate a legally binding agreement).
The reason formation of contract is more principle-oriented and not a fixed process is that fundamentally you can form contracts in any way you choose between yourself and another party, so long as it conforms to a number of principles - for instance, that you’re authorized to make that agreement in the first place, that there is consensus between you and the other person etc. Although some specific contracts may be regulated to be of a certain form and type.
I agree that the semantics around eSignature are still evolving and ambiguous. The industry is still relatively young and companies attempt to express their offering in different ways in the absence of a strong and developed vocabulary. Finally I would just say that nothing in this answer should be construed as legal advice. I hope this goes some way to answering your question.”