Rather than approaching the subject from a scholastic viewpoint, I looked into the meanings of the terms in every day business talk because these would reflect more closely our concerns in the enterprise.
The term chaos is used less than complexity in relation to the enterprise because of its negative connotations but it equally characterises the malaise of the enterprise today. To a degree indeed.
Looking at root meanings.
Complexity, comes from Latin denoting "entwined", "twisted together" while, linguistically,
Chaos, comes from Greek, meaning chasm or void.
According to Oxford dictionary,
Complexity" defines something as "complex" if it is "made of (usually several) closely connected parts" while
Chaos is defined as "complete disorder and confusion".
It is my view then that, in simple terms, complexity is characterised by structure, that is components and interconnections, while chaos denotes randomness, that is, little or no structure, order and, according to chaos theory, predictability.
Complexity does not equal chaos though, even if growing complexity may increasingly look like it, while chaos does not infere complexity.
Both concepts are relative, exhibiting degrees varying from less to more. Simplifying, "more" means more of a kind.
That is, more similar structures in the case of complexity and more diverse uncorrelated singular constructions in the case of chaos.
With "more" of both, a system is increasingly more difficult to control and change.
That is why both have to be set under control.
Complexity and Chaos in the enterprise.
A more complex enterprise has a larger number of functions and interactions. As such, it is harder to understand, model, control and change.
This source here explains it well: "A system would be more complex if more parts could be distinguished, and if more connections between them existed... Since the components of a complex cannot be separated without destroying it, the method of analysis or decomposition into independent modules cannot be used to develop or simplify such models. This implies that complex entities will be difficult to model, that eventual models will be difficult to use for prediction or control, and that problems will be difficult to solve. This accounts for the connotation of difficult, which the word "complex" has received in later periods".
A chaotic enterprise, on the other hand, has no clear structure while it consists of many singular functions, interacting ad hoc, rather randomly, standardless and procedureless. Similar inputs may result at times in different outcomes that are hard to predict in terms of duration and effort.
In short, in the enterprise, complexity manifests itself in the increasing number of functions and inter-relations while chaos is created by the proliferation of many different but unique functions and developments interacting at random.
The core issue is that both complex and chaotic enterprises are difficult to control, change and evolve, stalling as such the enterprise from keeping up with the business needs, markets, competition and rapid technology progress.
See also this post for complexity.