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.