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I am trying to replace the thumb-stick module on my Xbox one elite controller, because it started to drift. But, the solder on the thumb-sticks is not the same kind of solder as the wires that connect the rumblers to the controller. The solder is much different and does not come off with my soldering iron. I need major help.

@roseretro not quite sure where you see a difference. Attach a couple of images what you are looking at with your question. For that use this guide. It may help to clarify. To unsolder it you will have to have a hot soldering iron, some solder wick, flux and solder. Heat your soldering iron, clean the tip of course. Apply flux to the solder to be removed and the soldering wick. Then apply some solder to your hot soldering iron tip and place the wick over the solder and heat it up with your soldering iron.