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.
FLAC is the audiophile's handshake: CD-perfect sound at roughly half the shelf space. Free Lossless Audio Codec: think ZIP for sound: it decompresses back to the exact original. That makes it the right destination when what you need is archiving music with zero quality loss and a genuine size saving.