How do a heart murmur and a cardiac arrythmia differ?

2 different things. A murmur is a sound you hear with a stethoscope. It may be innocent or represent heart disease. An arrhythmia is an irregular rhythm which also may either be benign or serious.
Murmurs. Are associated with blood flow and valves and arrhythmia is a generic term for electrical system abnormaility.