Well, it depends upon how you define the words "fit" and "healthy".
I am inclined to say that you can be fit without being healthy; e.g. a world class athlete who has got the common cold may be very fit, but unhealthy because of the viral infection.
Also, I am inclined to say that you can be healthy without being fit; e.g. an old man who is very weak through lack of exercise, but may nevertheless be free from any pathological condition.
However, generally speaking, poor physical fitness tends to lead gradually to a deterioration in such things as: elevated blood pressure; atherosclerosis (narrowing of the arteries); cerebral thromboses; diabetes; etc.,
which many people would class as examples of ill health, typically caused by a prolonged failure to maintain good physical fitness, whether due to poor nutrition, inadequate exercise, or both.
Only insofar as I ought to be confined to a Mental Institution (or so I am occasionally informed).
Estragon , you seem well educated on the medical stuff, are you in the trade?