The offset distance is added in the view plane of the window where the user clicked the offset point. This means that it is usually best to apply the tool from the same viewing direction from which the curve was created.
The created parallel curve has an equal number of points with the original curve. Second order parallel curves (polylines) follow the original curve exactly at the defined distance. For higher degree curves, such as cubic curves, this is generally not possible. The control polygons are parallel but the actual curves may get closer or further apart at strongly bent curve sections.