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Whisper means - speaking in low voice and the speakers words could be understood.

Murmur is like unpleasant noise in which the meaning of the words spoken by the speaker may or may not be understood.

Whisper is when two person talks among themselves.

Murmur in sense the speaker speaks only to him or to any other person.
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If you mean whisper and murmur.
whisper:-speak very softly or a a soft or confidential tone of voice.
a low continuous background noise.
Whisper is talking softly to someone so that words are not understood clearly to others.
murmur is talking or muttering to oneself.