Supernovae (SNe) are classified based on their spectral features.  Type I SNe exhibit weak or no Hydrogen absorption, whereas Type II SNe show strong Hydrogen features.  Type I SNe are further broken down into subtypes based on the presense of Si II lines (Type Ia), Strong He lines (Type Ib), or weak He lines (Type Ic).

SN types Ib, Ic, and II are all the catastrophic deaths of large stars.  After exhausting all of their nuclear fuel, the cores of the most massive stars collapse into neutron stars or black holes.  The energy released accelerates the outer atmosphere away at very high velocities in a tremendous explosion.  Types Ib and Ic are thought to be fundamentally the same as Type II, except that the progenitor star has lost most of its Hydrogen (Type Ib) and Helium (Type Ic), most likely through tidal interactions with a binary partner.

Type Ia SNe, however, occur when a white dwarf in a binary system accretes matter it has tidally stripped from the companion star.  If the mass of the white dwarf exceeds the Chandrasekhar Limit (1.4 M₈), then the electron degeneracy pressure is overcome by gravity, and the white dwarf collapses.  The resulting explosion completely destroys the progenitor white dwarf.

Filippenko, 1997