Traditionally connected to a mercury manometer. Assumes that the external pressure on the artery is equal to the cuff pressure. Cuff needs to be longer than diameter. Intervening tissue needs to be flaccid, ie not tensed muscle. Long history, much data.
Inaccuracies do exist, but adequate for tracking changes with most medical conditions.
Oscillometry detects the small pressure changes in the cuff as the artery collapses and expands. Basis of modern automatic devices. Improve reliability by reducing apprehension and increasing number of measurements. Maximum sensitivity requires minimum compliance of cuff bladder. Only important example is tonometer for measuring intra-ocular pressure.