Prana is energy or nerve impulse. Vayu is a current of impulses. Breath alone has very little to do with pranayama , though the art of breathing is one of the means of bringing under control the 'Prana' ie.energy or nerve impulses. The real object of pranayama is to control the nerve impulses and nerve centres. It means , in other words , controlling of impulses received and directing of energy thus received. Pranayama is a process of bringing under control the autonomic nervous system over which normally we have no control.
Mistakenly pranayam is regarded as regulation of breath alone.
Pranayam is the art or technique of the control of the impulses by the help of many factors , of which , one such factor is breathing.