I would assume both home remedies and TCM arose for the same general purpose; save on affordability and availability of real doctors. By making yourself believe that honey on your chest after the second full moon of the year helps with laryngitis, you get some kinda placebo effect and then the news of it working spreads.

The difference is TCM is a multi-billion dollar industry from a country that cares little about human/animal rights, nor health and safety, nor regulation, and the leader of the country deliberately promoted it nationwide despite not believing it himself.

So it's had far more room to expand and become and earth shattering risk compared to that harmless mix of harmless spices in your cupboard that have already been regulated as safe by the FDA or whatever.

But, the psychological crossover is certainly there, you're right