Death of stars 

Giant phase

When the star has attend its full size it enters into a longest stage of life called as mid age and use their fuel (hydrogen) for millions to trillions of years according to the type of star. But when their starts ending up the stars with above 0.5 mass of our Sun become red giant or red supergiant and start fusing heavier elements like oxygen and iron. Their surface temperature decreases but their core due to pressure of gravity starts increasing its temperature.

Death

While upto here this is same for all stars with above 0.5 mass of our Sun. But their final death varies. Stars with 0.5 to 8 times the mass of our Sun gently shed their layers leaving behind a planetary nova and a dense core called as white dwarf which will shine for billions years.

While stars with above 8 times the mass of our Sun die in Explosive Supernova leaving behind a dense neutron star or a black hole.

In comparison of neutron star and white dwarf the white dwarf size can be like a Earth where as neutron star's size is lika a city but have mass of our Sun.