To mumble refers to speaking quietly in a manner that's difficult to hear. Muttering is the same except there's a tone of dissatisfaction or sarcasm. Many people use them interchangeably but there is a slight difference.

Mumble means to speak indistinctly (like a person with a cigarette in their mouth). Mutter means to speak to oneself at a low volume, possibly in a neutral tone, but often in an unhappy tone.

Если ваш босс говорит вам сделать то, что вы ненавидите = You might mutter to yourself. Если ваша жена задает вам вопрос, который вас не волнует = You might mumble a response. They are similar, and could be used interchangeably, but there is a difference in tone.

It is basically the same thing. I would not worry about it

Also, if you are muttering you typically don't want someone to hear you and understand you. Mumbling is speaking indistinctly which is difficult to understand, but you want to be understood. So a teacher might say to his student "Don't mumble when you answer!" (Speak loudly and clearly so that you are understood when you talk to me.) The teacher knew he was unpopular with his students because he heard their muttering. (The students made negative comments to themselves, such as "This teacher is terrible." These comments weren't addressed to the teacher.)