A spatial join operation that identifies the closest features uses the geometry method IProximityOperator::ReturnNearest to calculate distances. This method always computes straight line distances between geometries, regardless of their coordinate system.
ArcMap's measure tool calculates the length of each line segment as an ellipsoidal distance on a pre-determined representation of the earth. The results are aggregated to produce the distance value shown in the status bar. The measure tool returns an approximation of the path that the screen display line would follow along the earth's surface; this is not the Euclidean straight-line distance.