If I am "sick," I either have a cold or I am throwing up. Those are the only two times I use "sick" in reference to myself.

Bipolar is an ongoing condition, while 99% of colds tend to be short lived. So, I basically use the words "sick" or "ill" in reference to acute conditions where I am expected to recover fully. I think most people use "sick" and "ill" in the same manner, except in rare cases when someone is terminally sick/ill, but then again, people will still use the word "terminally" in that case to denote that they do not expect a loved one or person to overcome whatever disease they are ailed with.

Some people with bipolar do say they are "sick" when experiencing an episode, but even then, "sick" implies they expect to reach stability at some point.