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A projected separation is a calculated distance between two astronomical objects (their separation) based on the angular distance between them and some estimate of their distance from Earth, calculated as if our own distances to each were equal. The concept is used for objects close to each other on the celestial sphere and roughly the same distance and serves as a lower bound on the distance between them. As an estimate of their actual separation, it is no better than the accuracy of the determination of the distance to the objects. Furthermore, a small relative difference in the distance to each (e.g., a percent) can still result in an actual separation that is an order-of-magnitude or more larger than the projected separation. Objects for which projected separations are of interest include visual binaries, galaxies within the same galaxy group or galaxy cluster, extra-solar planets from their host stars, and other objects presumed to be (possibly) near each other, such as if they appear gravitationally bound.
I have seen the term projected distance used as essentially a synonym for projected separation but have also seen it quantified as milliarcseconds; if either of these terms is cited with angular units, they are surely being used to mean angular distance.