The Columbia Guide to Standard American English
These words are interchangeable and Standard in American English. In Britain, sick means “nauseated” or “vomiting, throwing up,” whereas ill is the general word for “feeling unwell.” Hence seasick has as its second part the British sense of sick. Like American English vomit, British sick can also be a noun meaning “the regurgitated matter itself.” There are possibly some occasional class nuances too: an American seeking to sound refined may more often use ill than sick, just as an illness may be thought by some to be a more elegant thing to have than a sickness.
Hello again, Here are some comments from a Canadian perspective. If I don't feel well, I'd say I am or feel sick, particularly in speaking rather than writing. If I feel nauseated, I'd say something like I feel sick or I feel nauseated.
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