I work as a Dr.
I am a Dr.
I am wondering if the two mean the same thing as well as whether the former is ambiguous.
Please fell free to ask me any question so as to specify the question.
Any comment or feedback would be highly appreciated
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Because "Dr." is a very special case, let's change your example to "cook".
(I'll explain the special case with doctors later.)
I work as a chef (=cook).
This phrase focuses on what the speaker does for a living. He may or may not have special training. You may assume that he was also trained as a chef if the dish served is excellent, but have no hint that this is the case, grammar-wise or liguistically.
I am a chef.
This may have different meanings, but mostly refers to how this person sees himself. It may mean that he was trained or that he works as a chef, but it may also mean that he cooks with passion. He may earn his living by cooking or not, this is unrelated.
Two examples that should clarify the difference:
I am a mother.
-> Obviously that is "who I am" not "how I earn my living".
I was trained as a chef, I worked as a cashier at the grocery store, as a mailman and as a bartender, but I am actually an artist.
-> all three varieties mashed in one example ^_^
So, in short: "working as" and "being" is very difficult to compare, because they focus on different aspects of life.
That said, choosing one version over the other in a professional context tells a lot about the speakers attitude and passion towards his job. I would always
Now about the "doctor" example:
Colloquially, for most people a "doctor" is someone who studied medicine and treats patients. For these doctors - let's call them by the precise term medical doctor or M.D., there are legal restrictions as to what training is mandatory before they may call temselves "doctor" and treat patients. So the distinction I explained in the main part of this post doesn't exist and the terms could be used interchangeably. I would strongly hope that the person I entrust with my health would use the "I am", though.
Also, note that most medical doctors do not work as "doctors" but as "general practitioners" or are specialized and therefore call themselves "pediatrician", "ophthalmologist", "gynecologist", "gastroenterologist",...
And, finally, note that there are many more that hold a doctorate degree, but may know less about medicine than you or me, but a lot more about chemistry, biology, astrophysics, psychology, the law or other fields of academic studies. They are doctors, too.