Sigh, sob, moan, groan are comparable as verbs when they mean to emit a sound, commonly an inarticulate sound, indicative of mental or physical pain or distress and as nouns, such a sound.
Sigh implies a deep audible respiration that is a usually involuntary expression of grief, intense longing, regret, discouragement, weariness, or boredom.
Sob implies a sound made by a convulsive catching of the breath when weeping or when both speaking and crying or when trying to restrain tears; the noun, however, more often refers solely to this sound than does the verb, which often implies accompanying tears and speech.
Moan implies a low, prolonged, usually inarticulate sound, especially one that is indicative of intense suffering of mind or body. The term, however, is often extended to sounds suggestive of pain, complaint, or murmuring.
Groan implies a heavier sound than moan and more often suggests an unbearable weight of suffering or a strong spirit of rebelliousness to pain or discomfort. Often however, in extended use the term carries no hint of suffering but implies noises made in strong disapproval or in pretended suffering or by something that moves or swings heavily.