[jacobolus]

Both chord length and arc length can be good ones. For some purposes versine (1 - cosine, sometimes called the "normal distance") and the half-tangent of arc length (i.e. the distance to one point when stereographically projected so the center of projection is the other point) are also useful types of quasi-distance. https://davidhestenes.net/geocalc/pdf/CompGeom-ch3.pdf