Also, psychiatrists may be biased towards diagnosing based on the symptoms that they can/want to medicate. For example, my Pdoc is officially treating me for PTSD. T doesn't think that I have "proper" PTSD, but the medication I am getting is helping me. Since Pdoc only writes scripts, I don't care if he knows the full picture. That's T's job. (I am on SNRIs + benzos, which are prescribed for a wide range of mood and anxiety disorders, so the exact diagnosis doesn't really matter in my case.)

If the difference in diagnosis is important in your case, I'd definitely follow up and try to coordinate between the two professionals. It might help to get a third opinion if possible.