Well, depends. Supernovae vary depending on their spectroscopy, and so we can deduce different types of supernovae. Most of them are core collapse, where yes, the star does collapse in on itself, the shockwave going outwards pushing all the material is what we actually see, where as the core collapse will create something like a neutron star or a black hole depending on the size of the progenitor. There is also another type of supernova caused by a white dwarf which is analogous to turning a hose on while spinning it in the air.