What are the stages of the death of a star? Are they different for different types of stars?
All stars die by collapsing under gravity. The process is different depending on the size of the star.
All main sequence stars are undergoing fusion reactions in their core. The fusion reaction produces a pressure which counteracts gravity which is trying to collapse the star. When the forces are in balance the star is aid to be in hydrostatic equilibrium.
Smaller stars with masses below 8 times that of the sun are fusing hydrogen into helium during the main sequence. When the hydrogen fuel runs out the star collapses under gravity.
As the core collapses it heats up to the point when helium can start to fuse into carbon and oxygen. The outer layers of the star expand to become a red giant.
When the helium fuel runs out and the core is mainly carbon and oxygen, fusion processes stop as the core can't get hot enough to start carbon fusion. The star then collapses into a white dwarf.
Theoretically, if the universe lasts long enough the white dwarfs will cool down over billions of years to become black dwarfs.
Larger stars over 8 solar masses start by fusing hydrogen into helium. Fusion processes fusing helium into carbon and then fusing heavier elements progress almost seamlessly.
When fusion processes produce elements lighter than iron energy is released by the fusion reaction. Fusing reactions which produce elements heavier than iron require additional energy.
When the core is mainly iron no further fusion reactions can take place. The core then starts to collapse under gravity. The pressure in the core reaches the point where atoms can no longer exist and the protons get converted into neutrons. This releases vast numbers of neutrinos which cause the outer layers of the star to explode as a supernova.
The core of the star is then a neutron star. If the mass of the core is large enough the neutron star further collapses into a black hole.