What is AAC?
MP3's designated successor and the audio in most video - YouTube, streaming services, broadcast, virtually every MP4. At a given bitrate it beats MP3 audibly, especially below 128kbps, and every phone and browser decodes it.
What is AIFF?
Apple's uncompressed format, the Mac counterpart to WAV, and still what Logic and older Pro Tools sessions expect. Its one genuine oddity is storing the sample rate as an 80-bit extended float, a data type almost nothing else in computing still uses.