To "mutter" is to speak in a low, indistinct, "hard to hear" way. Muttering is usually done by those who want to grumble or complain, but not necessarily want to be heard. To "whisper" is to speak in a hushed way, often near another person's ear, to share what is often a private matter. Whispering is associated with secret conversations and sharing topics that might embarrass you. Hope this helps