What is FLAC?
FLAC is lossless: it compresses audio to roughly half its size and gives back the original samples exactly, bit for bit. It is what people archive CD collections in and what high-resolution download stores sell. Sound quality is identical to the source; file size is not.
What is AAC?
AAC is MP3's designated successor and the audio in most video: YouTube, streaming services, broadcast and virtually every MP4. At a given bitrate it beats MP3 audibly, particularly below 128 kbps, and every phone and browser decodes it.