What are the different uses of MAC and Digital Signature? I know both of them can be used for Integrity and Authentication.
In which practical cases is preferred a MAC? and a Digital Signature?  

Thank you in advance
A MAC is a form of symmetric or secret key cryptography. It uses the same key for signing and verification. It's fast and produces a small signature. Almost all algorithms are post-quantum secure.

A digital signature is a form of asymmetric or public key cryptography. It uses the private key for signing and the public key for verification. It's slow and produces a slightly larger signature. The popular algorithms get broken by quantum-computers and the replacements all have significant downsides like large signatures.