In some contexts it makes sense to talk about angles between vectors that can span a full 360° because there is some natural orientation. As an example, for points on the unit sphere, we can assign unique angles over a span of 360° (the angle between a ray to that point and the x-axis) because we're oriented by the y-axis. If instead all we had was two rays with a common origin and nothing else to orient by, then we could only uniquely assign angles that span 180°.
Is there a common, succinct, and sensibly formal wording I can use to describe this distinction?
The best I can think of is to describe these angles as rotation angles (even if nothing is "moving").