"Chaos theory" was a term invented by the
popular press to describe the part of
dynamics usually referred to as
Chaos. To quote
Ian Stewart, "Chaos no more deserves to be isolated as a theory in its own right than "skeleton theory" deserves to be isolated from
zoology."
Nonlinear dynamics is the "newest" self-contained theory in this area, as it has recently taken off in its own right. When people say chaos theory, they often mean nonlinear dynamics.
As for a definition of Chaos, the following was proposed at a meeting of the Royal Society in 1986. It is hard to categorise such a new field, but this was the best attempt -
(Math) Stochastic behaviour occuring in a deterministic system.
This appears to be a paradox (stochastic means random), and can be paraphrased as "Lawless behaviour governed entirely by law." It is a common misconception that only complex systems demonstrate Chaos, when in fact something as simple as kx2 - 1 does.