I think we can over think the "taking" vs "making" concept.
To me a photograph is simply a snapshot or it isn't. Meaning a person made some decisions or they didn't.
A snapshot is seeing something, pointing the camera, and capturing it. That is "taking a picture".
As for "making a picture", the brain is fully in gear from the very beginning and the end result is already visualized. From that point on everything one does from camera/lens choices to eventually making a print, all are done to satisfy that pre-visualized image. And very often it is not what a casual observer standing beside the photographer sees of the same set of circumstances. The photographer sees the raw scene and already knows what he will do with it.
Where some people are confused is that these decisions are made in a millisecond and can to the casual observer, look the same as when a different photographer takes a snapshot.