Health
Personally i think health is about keeping yourself fit and prevent from diseases by eating and doing exercise BUT i was wrong.
World Health Organization(WHO)
health was defined as "a state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity".
It's not only based on disease itself but also the mental and social wellness. As conclusion we should also THINK right to keep healthy.
System
A set or series of interconnected or interdependent parts or entities (objects, organs, or organisms) that act together in a common purpose or produce results impossible by action of one alone.
Take ATM for example.......without the cards, machine and the software connected and working together we still can't take our money even if we don't have one of them.Right ??
p/s:Unless you have insufficient funds.
Health care system
From my point of view, i think that it is an organized plan of health service by which the health care is made available to the population. This is further optimized by government or private or both on the financial basis.
According to the WHO on the key component of health system are based on improving and defending the population from illness, protect them from financial consequences, providing equitable access to patients and making sure patients able to participate and make decision base on their health and health system.
As a conclusion, health care system is how the system work to make patients life better, the health providers become more efficient, and how the non-health providers help out make this one whole big system work.
1.http://www.who.int/about/definition/en/print.html
2.http://medical-dictionary.thefreedictionary.com/system
3.WHO:publication on key components of well functioning health system.