The digital certificate is a certification or electronic document issued by a Certification Authority (FNMT). It links a person with a public key, confirms his or her identity and allows him or her to carry out online procedures, including digitally signing his or her documents.
The digital signature is a cryptographic mechanism that, when applied to an electronic document, allows the receiver to identify the signatory and know for certain that the document is the original and, therefore, has not been altered.
With the digital signature you will be able to sign digitally and legally without the need of having a digital certificate issued by the aforementioned authority.