Ah. So it isn't just complexity after all. It is about the nature of the complexity. So now you just have to figure what the "nature" bit is and why it is such an important additional ingredient.
Complex systems are a particular type of systems. All systems are formed multiple elements interacting with each other. But complex systems are characterised by the high degree of integration and differentiation among the constituting parts. The integration of the system depends on a high interconnectivity and interaction between constituting parts. And the degree of differentiation is given by their degree of multiplicity and diversity.
Complexity then, is characterised by both qualities: integration and differentiation. Systems with either a low degree of integration or differentiation don’t behave like complex systems.
The relativity of complexity
Not all systems are equally complex. Complexity is relative and it depends on the degree of differentiation and integration, where higher differentiation and integration is related with higher complexity.
So we define the degree of complexity of a system as the degree of integration and differentiation of the system. High complexity is related to high degrees of integration and differentiation, while low complexity with the opposite.
Differences in the levels of complexity are also related with differences in the properties of systems and the way they behave.
Complexity