I don't know what's the difference in america but in british english, Sick refers to nauseous feeling as if you are going to vomit while ill refers to feeling of being unwell.

It depends on context. Both can be used interchangeably. But for me (in USA), I never use "I'm ill." If I'm feverish or have a cold, I say "I'm sick". There are other ways to use "I'm sick" such as: "I'm sick and tired of this ****." or "I'm sick and tired of your games". When used in this way "I'm ill" cannot be used interchangeably.

For me is the same meaning. "Sick" and "ill", are similars...

No, it wasn't a medical question... Why would I ask a medical question on a language learning website? It was only about the meaning of the words :)

Isn't this a medical question? Shouldn't you ask this on a different website? :)