[ Takakage inclines his head by way of a reply, though his smile is muted by the knowledge that both their families did not survive unscathed. ]

A hospital is a very large clinic - you can think of it as multiple clinics, in fact, each one specializing in a different area of medicine. Of course, there are general practitioners to field walk-in patients as well as more experienced ones in the Accident and Emergency department, but mostly it functions as a collective place for specialists to come together. Most sub-fields of medicine are connected, after all.