What is the difference between a type I and type II supernovas?
A type I supernova is caused by a white dwarf and a type II supernova is caused by a massive star.
Both types of supernova are caused by a star's core collapsing under gravity. When this happens temperatures and pressures increase until the point where new fusion reactions start. These fusion reactions can consume huge amounts of material in a short time which causes the star to explode violently.
A type I supernova occurs in closed binary systems where two average stars orbit around each other quite closely. When one of the stars exhausts its hydrogen it will enter the red giant stage and then collapse into a white dwarf.
When the second star becomes a red giant, if the stars are close together the white dwarf will accrete (=capture) material from the red giant increasing its mass. When the mass of the white dwarf gets to the Chandrasekhar limit of 1.44 solar masses its core will collapse. The collapse raises the temperature and pressure to the point where carbon fusion starts. A large amount ofd the white dwarf's material fuses in a short period of time the star explodes.
A type II supernova occurs in larger stars of around 10 solar masses. After it leaves the main sequence it starts fusing increasingly heavy elements in shells around the core. At some point the energy produced by the fusion process in the core isn't sufficient to overcome gravity and the core collapses. If the star still has an outer envelope of hydrogen, the core collapse will ignite a fusion process in the hydrogen layer which will trigger the supernova explosion.