A heading is the direction the plane's nose is pointed. A course is the direction it is actually traveling. The difference between the two depends on wind.
A true heading or course is corrected for magnetic variation; a magnetic heading or course is not.
Track and course are often used interchangeably, but technically a "course" refers to what you intend to do while a "track" refers to what you actually do.
ATC can only see your ground track on their radar screens, so logically that would be their reference for traffic advisories--and you may look in the wrong direction if you don't realize that, which I suspect was the point of the question.