Mumbling is talking inaudibly. The talking must be inaudible either because the volume is generally low or the person is articulating poorly. If the speech is inaudible because the person is not voicing vowels or voiced consonants, then it is not mumbling, it is whispering.
Praying generally means communicating or attempting to communicate with a deity or some other spiritual being: a boddhisatva, saint or the Tooth Fairy. It is quite possible to pray out loud or silently or in a mumble.
However, since most religions have a standard posture to take for praying, and standard forms of prayer, it is possible to look like you are praying when in fact you are on automatic and your mind is not paying attention to what you are saying. As you rattle off the standard prayer while thinking about that pot roast you are going to have for supper, someone might say to you, "You aren't praying; you're just mumbling."
The difference is portrayed in Shakespeare's play Hamlet. The murderous King Claudius, having been forcibly reminded of his guilt, attempts to pray. He gets down on his knees, clasps his hands, bows his head and his lips begin to move. Hamlet sees him and thinks he is praying. But Claudius afterwards ruefully admits that he couldn't keep his thoughts away from his worldly concerns. He wasn't praying, he was only mumbling.
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