I agree with Alyssa, and I would add that "brilliant" is a synonym for the other listed terms mainly in the U.K., not in the U.S. (though it is understood in the U.S.). -- In the U.S., "brilliant" is more often used to mean "highly intelligent" or "very bright" (either in terms of intelligence or luminance).

Just different ways of saying the same thing. Although some occasions one word may fit the sentence better. Brilliant, though, is a little less common and is usually used when someone is complimenting your ability to think outside of the box.