What is the difference between a cockatrice and a basilisk?

In terms of mythology, both are fairly identical. Both the basilisk and the cockatrice can kill with a glance, and both are said to be able to kill with poisonous breath. However, the difference between the two is this:

A basilisk is a serpent or frog egg hatched by a rooster, and is usually depicted as being more serpent-like. It also is fairly small, not bigger than six inches, in fact, however much the Harry Potter and the Chamber of Secrets movie tries to tell you otherwise.

There is also a real animal called a basilisk, for it's ability to walk on water, and the mythological basilisk is about the same size as it's real life counterpart.

A cockatrice, however, is a rooster egg hatched by a serpent or frog, and is usually depicted as being half rooster and half serpent, like in this picture: