Someone in healthcare explains why although these two words are used as synonyms, it would be helpful to make a distinction.
Apparently, the distinction was established in 1978, so this might explain why in everyday language people keep using them as synonyms.
Collocations with DISEASE
Collocations with ILLNESS
Post your Useful Language here, if you find sentences where these words are used in articles or audio texts. Example: http://www.naturalnews.com/illness.html and http://www.naturalnews.com/disease.html
Vocabulary exercises (though I think reading articles is much better and you learn more, too)
I just did the first, and it works. If you do any other, post your mistakes so we can double-check, You can also post the words you learned/learnt!