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I read this post Difference between MAC and Authenticated Encryption? but I'm still confusing the difference.

Seems like MAC can guarantee both integrity and authenticity (tbh I dont know the difference of integrity and authenticity).

What is the difference of MAC and AE? Is AE using MAC?

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Authenticated encryption also keeps the message secret.

Often, though not necessarily, authenticated encryption is built out of a composition of a cipher and a MAC—which, if you have to do yourself out of parts like AES-CTR and HMAC-SHA256, you should do as encrypt-then-MAC.

P.S. There is no substantive difference between authenticity and integrity. They both answer the question: Was this message sent by the party I expected to send it?

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