Contrary to popular usage, the two words do not mean the same thing. The difference is that orientation is rotation relative to some 'origin' orientation.
Orientation is a property, while rotation is an operation. It's like the difference between position and distance - "3 miles" is a distance, but you can't say "this point is 3 miles" - it doesn't make sense unless you say 3 miles from what.
So you can get stuck if you try and convert something like a quaternion (which represents a rotation) into a direction (which is a property). You can't do it unless you define your spatial system first - to say that (0, 0, 1) is 'unrotated.' Things just don't make sense otherwise.