In the case of a massive-star explosion, the core of the star may collapse so rapidly that it forms a sort of extremely compact (degenerate) matter. This compact object, which may be a neutron star or a black hole, is referred to as a compact supernova remnant. For both massive and white-dwarf stellar progenitors, the outermost layers of the star will be blown off by the force of the explosion into an expanding cloud of dust and gas. The shock wave and ejected material expanding from this explosion, and the interstellar material it sweeps up along the way, is called a diffuse supernova remnant.
A couple of the most famous supernova remnants are the Crab Nebula, a remnant of a relatively recent explosion; and Tycho, a remnant named after Tycho Brahe, who recorded the brightness of its original explosion.