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.
WMA is an abbreviation of Windows Media Audio. The WMA format is designed by Microsoft as an alternative to MP3. The WMA format is characterized by good compression ability and competes with the audio format from Apple AAC. This file format is supported by many portable audio players like the most widespread and common MP3.