Exporting an AAC to movie will embed the AAC into the movie with no further conversion.
Exporting an MP3 to movie will embed the MP3 into the movie with no further conversion.
All other formats will be converted to AAC.
If you need to use AAC instead of MP3, first export as PCM (AIFF, WAV) and then export to movie.
Movies are exported as .mov, but you can use ffmpeg to convert QuickTime MPEG-4/H.264 .mov file into .mp4 container.
Check this tool:
(the file is not re-encoded so this operation is very fast)