Spring: resorte or muelle?

Spring: resorte or muelle?
 

I keep hearing both. Is el resorte the spring that resists a push (such as a bed spring or a spring clamp) and el muelle the one that resists a pull (such as a spring that returns a door or gate to its closed position)?

If you look up muelle in the dictionary, you will find two definitions that seem at odds with one another, or so I first thought.

I have always heard and used resorte for the coiled wire used in mattresses, chairs and doors.

If you search for muelle in Google images, you'll see a whole bunch of piers. When you think about it, the most important use of a pier is to stop an advancing watercraft. The pier absorbs the shock of the impact so the craft isn't damaged. After all is said and done, a pier acts just like a spring does.
By the way, somewhere in the middle of all those images of piers, you'll find images of springs (coiled wire). :)

Also have a look here. It seems the two terms are both used, but I still believe resorte is more commonly used for the coiled wire.
To support that belief, have a look here and here. Both searches return similar images, but 'de resortes' has more hits.