Yes of course there are differences.
I'm not sure why you're asking me if a "core delusion" can be found in a case taken by a "Hahnemannian homoeopath". As I said above, I don't look for core delusions, and I'm not in a position to answer because I haven't studied that material in any depth.
I haven't felt the need to study it in any depth.
I can say that I followed up on a case in which Anti-matter 10M had been prescribed by another practitioner based on a core delusion that the patient felt "ungrounded" and which unfortunately left the patient quite out of sorts for some time with no signs of improvement. The Vital Force was regularized with three simple doses of Phos 30C in medicinal solution in a 100ml bottle, 5 succussions, one teaspoon from first cup, over 3 days, without a lot of hullabaloo. So I'm always left shaking my head when I hear statements like..."the polychrests don't work anymore, we need new remedies" or "we need to burn those 200 year old books and bring this science of ours into the 21st Century" which was said to me on the phone several months ago during a very-short-conversation. Breathtakingly ignorant imo, and the main reason I haven't attended an AHA seminar in years, as everything is geared towards presenting something new, and for me, the *new* factor is always found in some passage I never understood as clearly in the *old*.
I realize this probably hasn't answered your questions in the way you are seeking. I don't disagree when you say, it's a matter of discarding those methods which you personally consider unsound, but to me, this will always be a judgement call based on one's personal experience, as is - what comprises the main complaint in a given case, the Esse, the Wesen of the disease to be cured, and the characteristic value of symptoms.
While I obviously recognize the need for clear definitions, I'm averse to black and white applications of principles insofar as they negate, deny or dismiss real advancements in homoeopathy. Kent, for instance, in failing to completely understand Boenninghausen's methodology wrote an impressive Repertory of his own. <smiling diplomatically and I hope you are too>
I also think that it is a mistake to base one's opinion about a method if it has not been taught adequately in the first place. For instance, in the DL classroom we had the opportunity to briefly see how Ed Broussalian moved fluidly <I may have split an infinitive somewhere there> between rubrics in Kent's Repertory picking out redline characteristics, and explaining some finer points about how rubrics became Generals, and what the significance of a remedy being placed in particular rubric had in relation to it not being present in the General rubric, and at that point I knew for sure, that my comprehension of Kent's method was not, erm, as good as it can be. And I intend to improve on that.