I did a BSc in Physics. I consider myself a Physicist by education, just as I consider Musk to be. You are trained to be a Physicist whether you pursue a career in that field or not. As I mentioned on a post recently talking about research projects, my final year project in 1995, without going into too much detail, was modeling the expansion of the universe assuming a non-zero cosmological constant and tracing the paths of light through such an expanding/contracting/whatever universe, depending on assumed values, and studying the likely distribution of hydrogen absorption lines as it passed through a posited foam-like structure of walls and filaments of matter. This was a relatively off the wall topic at the time, but for anyone studying Physics today you'll know a lot of these things now represent the state of thinking in many ways. People might pursue these topics to a much deeper level in order to get a Masters or PhD but you still need to be a Physicist at any level to dive into such a project and produce a result.
At least that's my 2c - it's all just semantics, and as such there are many possible answers here :-)