This video shows what is lost when you convert your music to a lossily compressed format, such as MP3, M4A, or WMA. Although this video only shows the difference between a WAV (uncompressed) and MP3, similar results would occur if you compared WAV to M4A, WMA, or any other lossy format.
Generally, MP3 is regarded as an inefficient compression format. Newer standards like M4A, WMA, Vorbis, and Opus offer better quality for a given bit rate. However, with any form of lossy compression, some information is lost. Lossless compression codecs like FLAC and AIFF preserve quality; however, they do not reduce file size nearly as much as lossy formats.
When the WAV was converted to a 320 kbps MP3, not much information was lost. However, a lot of information was lost when the WAV was converted to a 64 kbps MP3.
It's 2017, and I think websites like Amazon and iTunes should no longer be offering only MP3s/M4As. With storage space so cheap and internet speeds so fast, lossless audio formats should be widespread. Lossy formats still have their uses, for example putting on a phone with little internal storage.