A binary star may, or may not, be related to a nova or supernova. In some specific cases, a supernova is specifically caused by a close binary system; but not all binary systems result in novas, and not all novas come from binary stars.

Matter can be transferred from the giant to the companion

That means that two stars are close together, orbiting their common center of mass.

A few are relatively close, like the ones that are in a binary orbit with each other, but most are LIGHT YEARS away from each other...

A binary star system is a system of two stars in space which are so close to each other that their gravitational interaction causes them to orbit around a common center of mass.