Although some medical historians have referred to Gully as a hydrotherapist, this is just the historians way of writing homeopathy out of history. Gully considered himself to be a homeopath, and while his staff provided various treatments to Darwin, Gully's treatment was primarily homeopathic medicines.
Note that in the letters above, Darwin refers to Gully's regime as "the Water Cure". Note that he describes Gully as acting as a "Hydropathist", who needed a second "doctor", one "Dr. Chapman", to provide homoeopathic treatment for his daughter. Note the description of Gully's regime in
this letter, from which you quoted the last time you told your Darwin story.