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An angular distance is the size of an angle between two directions from an observer, e.g., between two objects the observer can see. It is the angle between the observer's lines of sight to the two objects, and for large angles, if you extend your two arms pointing in two directions, it is roughly the angle between your extended arms. Angular distance is used as a measure between points on the celestial sphere, such as the positions of a pair of astronomical objects (e.g., stars). The coordinates of celestial coordinate systems are generally based upon angular distances, from reference points or reference great circles. In general, any angular unit can be used (e.g., radians) but typical in astronomy are degrees, either with decimal fractional degrees, or arcminutes, arcseconds, and/or milliarcseconds, etc., generally depending upon the size of the angle and the precision. Angular distance measurements between stars are fundamental to astrometry: accurate and precise coordinates of an astronomical object are calculated from measurements of angular distances between it and objects with well-established coordinates.
Terms such as angular diameter, angular radius, angular size, angular dimensions, and apparent dimension are used to describe extended sources, such as clouds or galaxies; for example the Moon's angular diameter is the angular distance of a diameter of the Moon's apparent circular shape in the sky.
I have also seen a quantity cited as a projected distance giving it units of milliarcseconds, which I take to mean angular distance, but I have also seen it cited with parsecs, suggesting projected separation is what is intended (which I find more logical).
The term angular size is also used solid-angle quantities, using units such as square degrees.