Changing the filename to have an .mp3 ending is like slapping a Volkswagen logo onto a Volvo.
It might *say* that it's a Volkswagen, but as soon as anybody so much as looks at it, it's kind of obvious it ain't.
m4a and mp3 are completely different encoding formats - m4a (aac) sounds better at the file size.
It won't burn your renamed .m4a files to an mp3 CD because - guess what - they aren't mp3s.
If you want to convert the files so they can be played on your mp3 CD player, you have to select the AAC files in question and then choose "Encode selected to mp3..." from the "Advanced" menu.
Note that transcoding from one lossy codec to another will further reduce audio quality.