M4A is AAC in a wrapper, MP3 is its older cousin
M4A files are MP4 containers carrying an AAC audio track and nothing else (no video). Apple uses .m4a to distinguish audio-only MP4 from video MP4, but technically you could open an M4A as .mp4 and most players would handle it. The audio codec inside, AAC, is the direct successor to MP3, designed to produce better quality at the same bitrate.
The conversion to MP3 is, in a sense, a downgrade by design. You go from a newer, more efficient codec to an older one with worse efficiency. The reason we do it anyway is compatibility: nothing on the planet refuses to play MP3, while M4A still gets the occasional "I cannot open this".
The naming confusion: .m4a, .mp4, .m4r, .m4b
Same container, different file extensions to signal intent. .m4a is plain audio. .m4r is an iPhone ringtone (identical to .m4a internally). .m4b is an audiobook with chapter markers. .mp4 with an audio-only track is what some non-Apple tools write instead of .m4a. Our converter accepts all four as equivalent inputs, decodes the AAC audio inside, and produces a standard .mp3 output.
The Voice Memos two-mode situation
iPhone Voice Memos has two recording modes: Compressed (the default, AAC at 32 kbps mono) and Lossless (ALAC inside the same M4A container). For voice transcription and casual playback, Compressed is more than enough. For conversion to MP3, both decode fine; the Compressed mode produces a smaller MP3 simply because the source has less audio information to re-encode.
Quality lost in the round-trip
Going from AAC 256 kbps (GarageBand default) to MP3 128 kbps does lose some audio fidelity. On consumer headphones or in a car, you will not notice. On studio monitors with critical listening to music, you might hear differences in cymbal attacks and other high-frequency content. For spoken-word audio at any bitrate above 64 kbps, the loss is inaudible even to trained ears.