My skeleton is complicated, I am complex. A convertible with reset, call / put features and soft calls is complicated, how to trade it is complex.
Complicated is when something contains many intricately combined building blocks, hard to figure out how it works.
Complex is something that acts as a system and it has properties and behaves in a way that are not obvious. We can understand how it works, but usually not predict what it does.
How complicated a thing might be, we can hope that we find a hard science approach, a scientific method to model its properties and behavior. This is what we do with derivatives and portfolio analytics. We apply computational finance emphasizing on blazingly fast model solvers, calibration engines in UnRisk.
Complexity happens on the small border between, kind of solid and liquid "aggregate" phases, or in other words order and chaos. Complex behavior often emerges from simple rules and programs (as fundamentally formulated in Stephen Wolfram's NKS)
One important segment in complex systems are those which are universal in the sense of programmability (like register machines - computers). They in general are "solid" enough to keep data persistent and fluid enough to transform signals.
Thinking about complexity in general, complexity economics, and econophysics approaches, like agent based models, for studying pricing formation and behavior of underlyers, I questioned myself whether our money system is programmable?
It is solid enough to store values and liquid enough to be the media for economic transactions.