Esign is typically a digital form of wet sign where the signer needs to sign a contract online instead of printing paper, signing and scanning through a printer.
It is consent driven where customers have to provide sanction through UIDAI received OTP. Aadhaar is just for eKYC purposes where a certified authority uses Aadhaar details to generate a digital certificate of the signature which can be used to sign a document. Aadhaar esign is issued by a certifying authority.