It depends on the context. In general, "to be sick" and "to be ill" can mean the exact same thing. Examples: 1) He was very ill. 2) He was very sick. These two sentences mean the same exact thing (the man was not feeling well or was suffering from some sort of illness). However, it can also be used differently in a sentence to imply that someone is either going to, is, or has already thrown up. Examples: 1) He drank too much and then got sick all over my car. 2) I feel like I'm going to be sick (or "get sick"). 3) The dog is getting sick on the carpet. Using this expression this way is very common in the UK, but not used very often in the US (though it can be used). Typically in the US, the verbs "to throw up" or "to puke" are used.

In my opinion there is no difference. "ill" is probably used a little more in writing (slightly more formal) whereas "sick" is probably used more in speaking, but the difference is virtually nonexistent. Sick is also used as slang for certain phrases like "that was really sick" (cool) or "that was a sick fall" (the guy fell down really hard. Another phrase that means the same thing would be "wiped out" like "he really wiped out"). It's not used too often that way though, and you wouldn't use the word "ill" for those cases. Also, certain words go together better than others. For example "fell ill" and "got sick" are phrases that are often said.