A measurement of the angular separation between a pair of stars does not necessarily tell us how far apart they really are. Although the two stars may appear close together in the sky, but one star may in fact be much farther away from us than the other. Thus the stars may in fact be much farther apart than they appear to be.
It is possible to calculate an separation in miles, km, or AU on the basis of the angular separation between a pair of stars, if the distance is known to one of the stars. The actual distance between the stars cannot be smaller than this "projected" value, but the projected separation in miles, km, or AU can be exactly accurate only if the two stars in question are both accurately at the same distance from the earth. If one star is farther away, the true distance between the stars may be much larger than the projected value.
The bottom line here is that to determine the actual distance between two members of what seems to be a double star system (or two stars of a multiple star system) requires more information than simply the angular separation between the two stars.