AAC or Advanced Audio Coding is an audio file format with losses. It was designed in 1997. as an MP3 successor with improved encoding quality. Its main advantage and difference from MP3 is a great efficiency of encoding at both constant and variable bitrates.
Apple Lossless also known as Apple Lossless Encoder is an open audio codec for lossless compression of digital music developed by Apple in 2004. Audio data is stored in an MP4 container with m4a extension. This codec is similar to other lossless codecs such as FLAC. Every year this format becomes more popular as it is used in iTunes and in all media devices from Apple.