It seems each of those words carry a different connotation with various people. Undoubtedly, the word doctor has lost a lot of what it means to the general population, as doctor can be a Ph.D as well a whole slew of people who help people with their health. It comes from a root that means to teach.
A physician has taken on the connotation of a formal medical doctor with a MD/DO degree generally speaking. It comes from the french word Physic which means remedy.
And then there is a healer. It is instructive to note that heal, whole, and holy are all related. Perhaps we understand this in some deep way anyway and it is why the term “healer” tends to evoke notions of holistic, alternative, healers.
Are these terms just playing with semantics? I don’t think so, I think what it shows that when it comes to helping people with their health, while the above terms are not that well defined, that the way to approach helping people comes from my different angles.
And with that, I have a patient waiting and when the door closes, the real world of person to person connection happens and if it is done right, all labels disappear and you are just there as a helper, person to person.