Student or Learner
does these words mean exactly the same?
I seldom find/ear the first one. is it too formal? should I avoid it?
what is the best word to express this idea (a person who is extremely self-confident and thinks he/she is the best)?
Good question! And not easy to answer.
In English North America, we don't hear "cocky" very often. Maybe that's because "cock" is the most common slang term for "penis."
When we do hear cocky, I think it's less insulting than conceited. It means confidant, optimistic, but perhaps in an annoying way.
Among Anglos, conceit is a serious sin, and there are many colloquial expressions:
I used to be conceited, but I got over that, and now I'm perfect. (ironic)
She thinks her shit doesn't stink. (vulgar).
She think's she's the cat's pyjamas. (slang, not common)
He thinks he's hot stuff. (slang, fairly common.
He's a smart-aleck. or (vulgar) He's a smart-ass.
You seem to be an intelligent person, jctgf.
But don't let that go to your head! (Don't get conceited!)
Greeting from Edward
the greatest English teacher on earth, the wisest, the most brilliant,
and also the most handsome.