What is the difference between a Type I supernova and a nova which are both in binary star systems?

Novae are white dwarf stars orbiting a companion star and accreting gas from the star. When enough lands on the bare surface, it flashes into thermonuclear fusion and detonates as a nova. Presumably, if the conditions are right, if the white dwarf is massive enough, the detonation can completely disrupt the white dwarf and you end up with a Type I supernova.