I use the term not just in the sense of a trademark, but more importantly to draw attention to a way of leading. I selected a chameleon for my logo because most people readily recognize it as a symbol of adaptation.
Adaptation is a dynamic process of mutual influence.
All creatures act on their environments, and their environments, in turn, act on them. We are all engaged in co-creation in our offices and in our families by virtue of the influences we exert on each other. Adaptive leadership is given to impacting the environment. It addresses a very active form of leadership, not a passive effort taken merely to adjust to circumstances as found. Biology teaches that relationships between living entities are circular and interactive.