Very good question. They are actually very different from each other. A Nova is when a white dwarf orbits a large star. The dwarf starts puling in gas from its companion and it builds up on the surface. As this happens, the surface gets hotter. Eventually, the surface gets to 10,000,000 degrees Kelvin which is the point where hydrogen fuses into helium. All the hydrogen on the surface of the star fuses at once and the dwarf star gets much brighter while it happens. From Earth, it seems that a new star is born so the Greeks named it a nova or a new. The dwarf star survives this and it may go nova many times in its life. Supernova however is the death of a star. It is usually the death of a large star but there is a type of supernova that occurs in small stars.
A Type 1a supernova is similar to a nova. Instead, the hydrogen builds up on the white dwarfs surface faster than normal. The temperature builds so much that it can fuse carbon (what most white dwarfs are made of). The star fuses all at once and explodes in a way that is almost equal in violence to the regular supernovas. The star is utterly destroyed in the event not even leaving a remnant.