In my opinion, or the way I would be inclined to use the words, I think it is a matter of degree. I'd say "I'm sick" if I felt nauseated and inclined to vomit, whereas I would use "ill" if I just felt poorly and inclined to stay in bed or take a pill of some sort. One would never say something was "sick-advised" or speak of an "ill-room", as another example of different usage.
Yes, 'ill' seems to have the additional meaning of bad, or evil. 'Speak/think ill of someone', or 'ill-timed'. Also, you can call in sick, but can't call in ill.
Is 'ill' an adverb in 'ill-advised'? I think 'sick' is a noun in 'sick room'.
One of my students asked me the difference, and I couldn't explain. Is 'ill' maybe an older word in English?
Originally posted by newnickname: Is 'ill' maybe an older word in English?
The OED gives both as Middle English. Ill is from an Old Norse word and sick from an Old English one which is related to Old Norse and other Scandinavian words. Ill, the noun, comes from ill, the adjective.
(There is a difference between English and American use of the word 'sick'. In American 'sick' is often used where we would use 'ill'. 'He is sick' is invariably 'He is ill' in England. )