Word Distinction: Degrees of Cleverness

In Britain, bright and smart (which is sometimes derogatory) are informal words for clever:

She is one of the brightest in the class.

He tries too hard to be smart.

But in the US, clever is often derogatory and bright and smart are used more often and more approvingly:

the smartest boy in class

She's very bright.

In both countries quick is an informal word meaning bright and able to learn fast:

Her children are very quick.

Brainy is an informal word which means very bright, often at academic work, but sometimes suggests that someone is rather odd and does not have a very good social life:

a brainy professor who is hopeless at parties

Brilliant is a very strong word meaning extremely bright:

He's a brilliant mathematician.

Clever clogs is an expression used to someone when they have just made what they think is a very clever remark or suggestion:

"Put it in the other way up." "I tried that an hour ago. Come on, clever clogs, you can do better than that!."