These words relates to Health category. I think these words are really confusing and I don't know how to use them correctly. Can you show me what are the differences between these words?
These terms are used with more precision by healthcare professionals than by the general public. The dictionary definitions reflect general usage of the terms.
Remedy as a noun is often applied to health, but the verb isn't commonly used in that context. It means to relieve a problem, which is very imprecise if you apply it to health matters.
Heal and cure are related:
Heal and cure refer to the patient, although "cure" is often used in the broad sense of eradicating a class of illness from the population at large, like "curing cancer". But if a person has an illness, you cure the patient, not the illness.
Also note that heal and cure refer to accomplishing the result rather than the nature of the process. The "curing" or "healing" done by the doctor might be little more than keeping you comfortable while your own body does the work, but they are said to have cured or healed you because they provided the conditions to bring about recovery.
The difference between the terms focuses on the nature of the problem. Health problems that are not based on a deficiency of something the body needs (and can be fixed by providing that), are broadly categorized as injury or disease. Injury is physical damage. Disease is a condition that impairs normal functioning. This isn't medical school, so I won't get into the weeds with rigorous definitions.
"Cure" refers to disease (you don't cure injury). In common usage, "heal" is applied to disease or injury, but it more accurately applies to injury or the physical manifestations of a disease.
It refers to the application of treatments, not the results. Again, you treat the patient, not the problem. In common usage, people say things like "treat a cold" or "treat a broken arm", but that's shorthand for treating a patient for a cold or for a broken arm. There is no guarantee that treatment will result in healing or cure.