There really is only two ways to ventilate a patient, using (conventional) positive pressure or negative pressure. Some of the earliest respiratory ventilators were negative pressure chambers.
A severe poliomyelitis epidemic broke out in Northern Europe in the mid 1950s. Patients suffering with this virus die from asphyxia - respiratory muscle paralysis and failure to ventilate. Medical students were assigned to manually ventilate paralysis victims until restoration of neuromuscular activity occurred. Iron lungs mimicked the chest cage's activity in generating minute ventilation, but were of little value in diseases characterized by failure to oxygenate. The machines were bulky, expensive and somewhat unhygienic.
The first positive pressure respiratory ventilators were pressure controlled. This made sense as the chest is a negative pressure ventilator. Volume controlled ventilators became ubiquitous in the 1960s as this mechanism was perceived to be more reliable at delivering minute ventilation, and thus normalizing blood gases.