The two words mean exactly the same thing. "Whilst" is very common in the UK, and common in Canada. "Whilst" sounds quaint to Americans. (I'm not saying it is, just that it sounds unusual to the American ear.) "While" is the only form used in the USA. "While" is also fine (not strange) to use in Canada or the UK. So: If you would like to speak UK English, use "whilst"; otherwise, "while" is a better choice.

They have the same meaning. In American English we tend to use "while. In British English you'll hear "whilst" more often.

Most of the time they are the same,. Whilst just sounds more formal.