According to SN, the major difference is that e-Signature is NOT an embedded signature, while document template signing is.
Also e-Signature is SN signing only, while document templates support basically any signer, like SN, Adobe, DocuSign and many others.
With Document Template signing one starts with a (PDF) document where space is reserved for signing, it is submitted to the signing authority, the signing authority adds the signature as you sign it and returns the same PDF document with signature added for further processing (i.e. storing it as an attachment somewhere); sometimes the signing authority/broker also provides some proof of signing records and - of course - keeps a proof document for itself.
