I've noticed that British English speakers use "ill" more frequently than American English speakers. My British friend uses "ill" frequently, but I almost never say it.

For the most part they could be used interchangeably. I guess for a better distinction between the two, being "ill" could refer to you just not feeling the best or not 100%. Being "sick" would refer more to actually having some kind of disease in your body that would cause you to vomit, sneeze, cough, etc. But in actuality you could get away with using either one in a sentence and a native would know which one you mean. Hopefully that helps!