When I studied P.E. the definitions were
Health: the general well-being of the body systems and good overall functioning of the various body systems and vital organs
Physical Fitness: the ability of the body to meet the demands of a given situation, as relevant to the individual
Specific fitness: the ability of the body to meet the demands of a particular sport and its fitness components
General fitness: the overall basic fitness of an individual who can meet the demands of everyday life
Motor fitness: the ability of the central nervous system to work with the body to produce quick, precise and accurate movements
And just "fitness" was defined as all of those put together. For example, a mate of mine is an ex-sprinter, specializing in 100m. He can still run it in about 10.3 seconds, but his stamina is awful. And he has bad knees (why the ex part). So he has specific fitness, but not general fitness or health.
There is also a big social and mental side to fitness. For example, you can be as physically fit as you want, but if you're suffering from depression and have no friends, you probably wont perform too well.