Brent,
No, there is no definition for Fairway or Rough in the rules. Also, I think there is rather significant leeway in the definition of putting green, which reads something along the lines of, "Any ground specifically prepared for putting," or some such verbiage. I feel as though one could make a rather strong case that marking a ball on a collar is marking a ball on a "ground specifically prepared for putting," but to my knowledge nobody has pressed the matter.
Rule 25-2 addresses embedded balls stating that a "closely-mown" area is any area at fairway height or less. This seems rather vague as I feel a good argument could be made that any well-maintained and uniform turf, regardless of length, is "fairway." The use of the term fairway implies some sort of definition somewhere, with the only really distinguishing characteristic of fairway being height of cut.
I think the verbiage is such that the USGA does not start defining or codifying actual maintenance practices within the Rules of Golf. That way any golf course can maintain as they wish. I agree with this and we are in trouble if the USGA ever attempts to standardize maintenance practices de jure. However, the embedded ball situation implies a de facto definition, based on a maintenance practice. Slippery ground.
I am curious of the origin of the term fairway. Did it imply that balls stopping in this area would generally find similar conditions across it? If so, why the avoidance of codifying fairway and rough within the rules?
That being said, and as Tom Doak notes, this is a search to get back to these ideas (Rough/Fairway, et. al.) that I believe came out of the attempt to move the game inland from the linksland.