WAV is a container format for storing a record of a digitized audio stream without any compression. This format was developed by IBM and Microsoft in 1991 and was used in all versions of Windows. As the format uses audio streams without any compression, the files become very large in this format.
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.