While the terms are often used interchangeably, there is an important difference to recognize.
Electronic signatures, or eSignatures, refer broadly to any electronic process that indicates acceptance of an agreement or a record. This can mean typing a name or drawing a signature with a mouse with no added level of trust or security.
The term digital signature is reserved for a specific subset of electronic signatures that uses a certificate-based digital ID binding each signature into the document with encryption. This is to authenticate the identity of the signatory and demonstrate proof of signing.
Electronic signatures can also have extra levels of security to them involving officially issued electronic certificates, as defined by the eIDAS regulation - see advanced electronic signature and qualified electronic signature.