Nova are produced in binary star systems in which one of the two stars is a white dwarf or a neutron star, and the other is a normal star usually a red giant which has a distended outer atmosphere. Some of this material can be captured by the dense companion via a process called Roche Lobe Overflow. Depending on a variety of factors, the dense companion will flare up as a nova periodically, or simply blow itself to pieces as a 'Type I Supernova'. The dynamics of the nova process are sufficiently complex that we as yet have no good way to predict when outbursts will occur from a 'cold start'.
Supernova are explosions that detonate the entire star.
Some of these are nova-like situations such as the Type I event above. We have good theoretical reasons to believe that supernova precursor stars will be red supergiants if their heavy element content is like that of the Sun, or perhaps blue supergiants if they have somewhat more heavy elements as was the case for Supernova 1987A in the 'metal-rich' Large Magellanic Cloud. The star just before it becomes a supernova may have a composition that suggests a great deal of chemical enrichment of its surface by convection from its nuclear core. There may be a sudden increase in the velocity of its stellar wind, and the thickness of its circumstellar dust envelope. As we learn more about the theory behind the explosion, we can better anticipate just what kinds of things to look for observationally.