these are 'rough' estimates, and there is some variation in opinion as to where exactly these boundaries should lie. The final events in a star depend on more than just mass, although its mass is the single most important factor.
Stars with masses of 0.4 though about 8 solar masses will end in a white dwarf + planetary nebula. Stars below that limit are 'red dwarf' stars, which are extremely long lived, in part because they never achieve fusion through the triple-alpha process, instead using only the slower proton-proton chain process.
Stars with masses between about 8 and 20 solar masses (again, the exact boundaries are uncertain) will end up as neutron stars after undergoing a type II supernova.
Above 20 they do the whole 'black hole' thing.
