M4A is AAC in Apple's favorite outfit: the audio-only MP4 your iPhone speaks natively. It was born in 2003, popularized by Apple's iTunes Store, and its real weak spot is older Windows software and stubborn car stereos that expect a .mp3.
AAC is MP3's better-trained successor: cleaner sound from the same number of bits. Advanced Audio Coding: the default soundtrack of YouTube, iTunes and most MP4 video. That makes it the right destination when what you need is streaming-grade sound at friendly file sizes.