For example, I can say "used for storing fat", or "used to store fat". What is the difference between the two phrases?
These two sentences:
The lizard's tail is used to store fat.
The lizard's tail is used for storing fat.
mean exactly the same thing. The s in used is pronounced soft, like a z. In IPA, that's /juzd/.
An auxiliary verb
The lizard used to store fat in its tail, before the mad scientist altered its metabolism.
or more realistically:
Mom used to bake cakes all the time, before she gave up eating sugar.
Your jokes used to be funny.
Many people pronounce the s hard (unvoiced) in this sense of used to, resulting in this pronunciation: /just tu/ or even /jus tu/. Used for cannot be used in this sense.
A synonym for accustomed to
Used to also can mean the same as "accustomed to", as in these sentences:
My mom's cakes taste terrible at first, but you'll get used to them.
The lizard is used to living in a cage.
Many people also pronounce this sense of used to /just tu/ or /jus tu/. Used for does not have this sense, either.