Not alot, ill is more formal however. They can also be used the same way in slang contexts to mean "extremely cool". Most of the time they just mean sick as in under the weather. Illness and sickness are also both the same.

"ill" can be an edjective, an adverb, and a noun. - He felt ill, so his mother sent him to the doctor. (as an edjevtive) - I can speak no ill of her. ( as a noun) - He can ill afford the money. (as an adverb) "sick" can be an edjecktive, a noun, or a verb. - I am sick of his everlasting laughter (as edjective) - I am sick and tired after work hard. (as a verb) - The sickness must be treated by a doctor.( as a noun)