This is less a math question and more a semantic one. Suppose A and B are two arbitrary axes and I'm interested in an angle of a vector emanating from the origin. If I refer to vector's "angle between A and B" does this grammatically mean that the A-axis points right, the B-axis points up and the angle is traced counterclockwise from A to B? Thus, if I referred to the vector's "angle between B and A" then the axes would be flipped: B would be what is traditionally the x-axis and A would be the traditional y-axis.
I'm afraid I might be off here...as in this phrase structure could be informal and may have no standard meaning. If that's the case, how should I distinguish between these two angles? (I'm assuming the axis names are fixed and can't just be relabeled however is most convenient.)
By convention, an angle is always measured as increasing in a counter-clockwise manner, and decreasing in a clockwise manner. For a fractional circular measure which increases clockwise and decreases counter-clockwise, the correct terminology is a bearing. So if you were to report a fractional circular measure of direction of a vector $\mathbf{v}$ which increases from the $y$-axis in a clockwise manner, you could say, "The vector $\mathbf{v}$ has a bearing of $57.3^\circ $ [to the $y$-axis]," where [to the $y$-axis] can be omitted if there is a convention that is made obvious. I have never seen the term bearing used mathematics, since we can easily give a negative angle. However, it is frequently used in real world navigation, where the convention for the $y$-axis is North.