My definition of health and illness is based purely on an individual by individual standpoint. There is almost no way to set certain criteria that each person can follow to determine whether they are healthy or ill. If a person has certain limitation such as asthma, but does not let it bother him then I would consider that person healthy. However if someone does not have asthma but is rather just extraordinarily out of shape and seeks help for it, that person would be considered ill. Health/illness, unlike disease is something that is purely subjective.
My first “condition” I chose was old age. It is pretty strange to think of old age as being an illness, seeing as it is inevitable for anybody that lives long enough. There are also plenty of old people with no problems that live their lives very happy. However, I believe old age can be an illness if that individual feels inhibited by it. Old age can help in causing other aliments such as achy bones/muscles and diseases such as Alzheimer and dementia. If an old person feels that the fact that they are old is inhibiting their life, and they seek a professional to help them with whatever it may be, pills, therapy, etc then I would consider that their old age is an illness.
Erectile dysfunction is another condition that may not be quite as it seems. Many people would agree that erectile dysfunction is not something that a man would want and is definitely something that needs to be fixed, or is it? Some men may not be very sexually experienced while having erectile dysfunction so they believe that nothing is out of the ordinary. These people could fall into the “diseased but not ill” category as something is physiologically wrong with their body, but they do not feel the need to seek help for it. Another person where erectile dysfunction would not negatively impact their life is someone who has abstained from sex, such as a monk. They have no need to get a boner and therefore should have no reason to think they are sick. However, for most men erectile dysfunction is a horrible condition that they try to cure immediately as it can cause a lot of psychological drama to them.