Naga and Sarpa both mean snakes in Hinduism. But there is a difference between them. Nagam or Naga and Sarpa or Sarpam are worshiped by Hindus from ancient times. Today nagas and sarpas are often used synonymously.
Nagas are semi-divine and have powers. Sarpas are not divine and do not have any powers.
Nagas can assume any form at will. Sarpas do not have this power.
Nagas have a world of their own in the nether world. Sarpas do not have a world of their own and therefore they live mostly on earth.
As per Harivamsa, Vasuki is the king of Nagas. Takshaka is the king of sarpas.
Nagas are commonly associated with Shiva, Vishnu and Devas. Sarpas are most associated with demons and they seem to have some negative qualities.