Ill Britney Pulls Out Of Mtv Awards

What is difference between ill and sick, how do i say sick people or ill people to refer to people not feeling well? I want to apologize for some mistake in official mail and want to make them sure i will not do that again. I will take care of this next time.

While those might mean the same for the laymen, from a medical point of view, there is a difference between illness and sickness. Medical sociology has long made the distinction. Is it correct to think that if i say i have been ill for a week it could both mean i am still ill or i just got better? I thought that if you have recovered you should say i was ill for a week.