What is the difference of "Sick" and "ill"?

In the medical sense, they mean almost the same thing, and in most cases they may be used interchangeably. Ill might be slightly more formal.
There is a grammatical difference, If you are sick and get worse, you can be sicker. Ill does not have a comparative form in the same pattern. "iller" is not standard English. If someone is ill and gets worse, you just have to say, "He has gotten worse."

In other uses, the difference does not follow any pattern.

You would say, "An ill wind," meaning it brought some misfortune. A "sick wind" doesn't have any meaning.

Likewise, if you don't like something, you might say, "That s sick." Il"l won t do here.

English does not have consistent rules for things like this. Each expression must be learned.

Sometimes they mean the same, but ill will be more formal such as when you speak to your boss:
I am ill today, and I won't be able to come to the office.
Please excuse my child for his absence. He was sick yesterday.

Sometimes they have different shades of meanings:
I am sick of your nagging at me to get a new car. [It means you are bothering me.]
I felt ill when the elevator suddenly stopped, and I had to be rescued. [It means I was so frightened.]
To me it is sick to lock up a child in a closet for misbehaving. [It means it is sadistic.]
He robbed the bank, and now lives on his ill gotten gains. [Here ill means dishonestly.]

now there's a "can of worms".....

Sick sometimes implies a tendency to vomit, or a trait you also have when you are fit as a fiddle

ill always is just a medical thing, your immune system battling some germs. Oh wait, there's also such a thing as "ill repute"

Sick can mean cool, as in "You look pretty sick, bro!"
Ill does not mean cool.

Actually: What is the difference between "sick" and "ill"? "Of" is wrong there.

In Britain the difference would be social, almost "class", but then, almost everything in Britain is connected with social class!

What is the difference BETWEEN "sick" and "ill." They mean the same thing.

What is the difference BETWEEN 'sick' and 'ill'.
Generally, 'ill' is the more formal medical term, but it has other uses too, as in 'ill-gotten gains' and 'a person of ill repute'.
'Sick' can mean ill, but it can also mean vomiting. 'Excuse me, must run; I think I'm going to be sick!' means 'Get out of the way and let me rush to the bathroom; I'm about to vomit'. 'My child was sick four times during the night' = she vomited four times.

They have the say meaning. There is no hard and fast rule as to when one or the other should be used.

They're pretty much the same

Basically, there isn't one, though they can be used in different ways.

You'll find that "sick" is more often used figuratively. People can be "sick and tired" (fed up with) of something, or something "makes them sick" (i.e., they find it disgusting or awful.) "Sick" can even be used positively, as slang for something unusual that someone admires: "Wow, that's really sick!")

You'll also find that people who speak slightly more pretentiously tend to prefer "ill" over "sick".

But fundamentally and normally, they both refer to medical condition.