Basically, both hairspray and hair lacquer are hairsprays. The difference lies in the specialisation. Hair lacquer is a further development of hairspray and is used to emphasise individual parts.
While hairspray has the function of giving the hair styling the final touch, hair lacquer is usually only used in sections or strands. Hair lacquer is intended to strengthen and emphasise certain sections of the hairstyle or to create unnatural shapes - such as updos or spikes.