From an end user's point of view, there is no difference in the orientation. But from the device's point of view, one orientation has pins 1-8 and the other has pins 8-1. It's up to the device to figure out which is being used. This is still considered symmetrical though.
I get the point you're trying to make, but the connector is electrically symmetrical: "made up of exactly similar parts facing each other or around an axis"