AAC is MP3's better-trained successor: cleaner sound from the same number of bits. It was born in 1997, an MPEG all-star team: Fraunhofer, Dolby, Sony, AT&T and Nokia, and its real weak spot is older or stubborn hardware that only ever learned MP3.
WAV is audio with nothing taken away: every sample intact, every megabyte accounted for. Raw PCM samples in a RIFF wrapper. No compression of any kind. That makes it the right destination when what you need is recording, editing and mastering, where every last bit matters.