What are the similarities and differences between pulsars, quasars, white dwarfs, neutron stars and black holes?
Pulsars, white dwarfs, neutron star and black holes are the remains of dead stars, quasars are powered by black holes.
When a star less than about 8 solar masses runs out of hydrogen and helium fuel, its core isn't hot enough to start carbon fusion. The core which consists of mainly carbon and oxygen collapses under gravity to form a white dwarf. Gravitational collapse is stopped by electron degeneracy pressure.
If the star is larger than about 8 solar masses it is able to fuse heavier elements up to iron. As iron fusion required energy rather than releasing it the fusion reactions stop and the stellar core collapses under gravity. It the core is more massive than the Chandrasekhar limit of 1.44 solar masses gravity overcomes electron degeneracy pressure atoms can no longer exist. Protons become neutrons and large numbers of neutrinos are emitted causing a supernova explosion. The star's core become a neutron star.
If a neutron star is spinning and has a strong magnetic field it emits radiation. As it spins at a precise rate the beam of radiation its the Earth periodically with a period of milliseconds to seconds. This is a pulsar.
If the stellar core is more than about 4 solar masses gravity overcomes neutron degeneracy pressure. Once the core collapses below its Schwarzschild radius, spacetime is curved to the point where not even light can escape. This is a black hole.
Most large galaxies have a supermassive black hole at their centres. These are in excess on hundreds of thousands of solar masses. If there is a good supply of gas and dust in the vicinity of a supermassive black hole it forms an accretion disc of material falling into the black hole. Material falling into the accretion disc gets superheated by friction and gravity to the point where it emits huge amounts of energy. This is a quasar.
So, all are similar in that they are formed from the remains of dying stars. Pulsars are a type of neutron star. Neutron stars and black holes behave similarly. The main difference between these objects is mass.