Difference between MAC and Authenticated Encryption? I am currently studying authenticated encryption and I was wondering if there was a difference between using a MAC and authenticated encryption.  It seemed like authenticated encryption schemes use MAC's in order to provide a level of integrity to the ciphertext.

However, I was unsure if there were specific modes of operation for different ciphers that inherently provided a level of authenticated encryption or if a MAC was always necessary to provide authenticated encryption?

Any examples would be of great help.
A mac is basically applied after encryption is totally complete, where "authenticated encryption" usually refers to something like a mode of operation that builds an authentication tag as the process of encryption moves along. The goal of the "authenticated encryption" is basically doing the same job as a mac in less passes/applications of crypto primitives.

Examples of "authenticated encryption" include GCM mode and the duplex mode offered by the sponge construction. Using either of these will produce an authentication tag with the ciphertext. If data was encrypted using either of these, then application of HMAC after encryption is not necessary.

Suppose a mode of operation like CBC was used instead. It does not produce an authentication tag, and in order to assure integrity and authentication we would require the application of HMAC. This must wait until after encryption was complete. Because this is essentially two totally separate operations, it is relatively slow compared to GCM mode.