In a nova, a layer of hydrogen is pulled from a regular star, forming a kind of dense atmosphere around the white dwarf. This atmosphere is heated by the novawhite dwarf, until a critical temperature is reached, and fusion begins in the atmosphere. The white dwarf is rather unaffected by this, and the process of forming a hydrogen atmosphere can restart. Recurrent novae are well known.
In a type 1a supernova, the mass of the white dwarf increases towards the Chandrasekhar mass, of about 1.44 sun-masses. At this point, the degenerate carbon and oxygen, which the white dwarf is mostly composed of, begins to fuse. The energy released is enough to completely unbind the white dwarf.
In a nova it is only the hydrogen atmosphere that explodes. In a supernova it is the whole carbon-oxygen star.