CAE means “Christians affirming evolutionary science”. I would say that it is a general term for self-identifying Christians who affirm the methods and conclusions of mainstream evolutionary biology, cosmology, geology, and other sciences, without necessarily assuming any particular sort of model of interaction between the Creator and Creation.
CAE is my newly preferred term because “evolutionary creation” or “theistic evolution” tends to bring with it some historical baggage about assumptions regarding interpreting Scripture, whether miracles can happen, etc. As a CAE, I tend to disagree with ID-type arguments in science, but I don’t necessarily shirk back from the possibility that God governs natural processes, including evolution.