Hi Bill,
Possibly one reason for a spring being so called is that such a mooring can be used to "Spring" a vessel off her berth. In the above picture for example. if all moorings are cast off except the for'd spring (Bow spring) and the rudder put hard over to port & the engine put to dead slow ahead, the spring will hold the bow onto the quay and the stern, and thus the propeller, will come clear of the quay. In an old fashioned single screw ship with no bow thruster this method was, and is, regularly used to take a ship off her berth without the aid of a tug. We always called the springs the for'd and aft backsprings. The addition of the "back" is self explanatory.
Sadly the mooring set up in SSE makes it difficult to do this sort of thing, but SS 2008 was excellent for doing such things.
Regards,
Angus.