A digital signature is a method that can be used to verify the authenticity of a digital document. Typically, a digital signature system uses three algorithms. To generate a public key/ private key pair, it uses a key generation algorithm. It also uses a signing algorithm, which generates a signature when given a private key and a message. Furthermore, it uses a signature verifying algorithm to verify a given message, a signature and the public key. So in this system, signature generated using the message and the private key combined with the public key, is used to verify whether that the message is authentic. Furthermore, it is impossible to generate the signature without having the private key due to the computational complexity. Digital signatures are mainly applied for the verification of authenticity, integrity and non-repudiation.
A digital certificate is a certificate issued a CA (Certificate Authority) to verify the identity of the certificate holder. It actually uses a digital signature to attach a public key with a particular individual or an entity. Typically, a digital certificate contains the following information: a serial number that is used to uniquely identify a certificate, the individual or the entity identified the certificate and the algorithm that is used to create the signature. Furthermore, it contains the CA that verifies the information in the certificate, date that the certificate is valid from and the date that the certificate expires. It also contains the public key and the thumbprint (to make sure that the certificate itself is not modified). Digital certificates are widely used on websites based on HTTPS (such as E-commerce sites) to make the users feel safe in interacting with the website.
A digital signature is a mechanism that is used to verify that a particular digital document or a message is authentic (i.e. it is used to verify that the information is not tampered) whereas digital certificates are typically used in websites to increase their trustworthiness to its users. When digital certificates are used, the assurance is mainly dependent on the assurance provided the CA. But it is possible that the content of such a certified site could be tampered a hacker. With digital signatures, the receiver can verify that the information is not modified.