"FEELING SICK" ≠ "BEING SICK" 
ILLNESS = our emotional, psychological, and/or spiritual REACTIONS to our sickness.
Spiritual care seeks to HEAL your illness.
SICKNESS = part of the body (or mind) is broken or malfunctioning.
Medical care seeks to CURE sickness
"These patients felt the pain of their sickness,
but little or no discomfort from an illness. "
ref: healyourillness.com
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Illness is very similar to DISEASE in everyday speech...
a disease is typically perceived as a more serious or incurable problem (e.g. a genetic disease).
While an illness, on the other hand, is simply the cause of a temporary state of ill health...
ref: wordreference
Sickness is a generic term referring to a condition you experience when do not feel "quite well". Sickness may refer to being nauseated (e.g. motion sickness) or just being unwell because you are ill or tired.
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according to a dictionary:illness /ˈilnis/ [noun] -
a disease or period of sickness affecting the body or mind :
he died after a long illness
I've never missed a day's work through illnes.
sickness /ˈsiknis/ [noun]
1 the state of being ill : she was absent through sickness.
• [often with adj. ] a particular type of illness or disease :
botulism causes fodder sickness of horses / a woman suffering an incurable sickness.
2 the feeling or fact of being affected with nausea or vomiting :
she felt a wave of sickness wash over her | travel sickness.
disease /diˈzēz/ [noun]
a disorder of structure or function in a human, animal, or plant,
esp. one that produces specific signs or symptoms or that affects
a specific location and is not simply a direct result of physical injury :
bacterial meningitis is a rare disease
a possible cause of heart disease.
• figurative a particular quality, habit, or disposition regarded
as adversely affecting a person or group of people :
departmental administration has often led to the dread disease of departmentalitis.
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