A star's death method is determined by its mass. A star with a mass under 4.2 times the mass of the Sun (called the Chandrasekhar limit after the University of Michigan astronomer who first determined it) will wind up a white dwarf and ultimately burn out as a heavy but small, dense object.
More massive stars will become white dwarfs, neutron stars, novas, supernovas, black holes, depending on a variety of factors, including mass and the presence of a close stellar binary companion