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Polarizable means an atom's electron cloud can be easily distorted by the strong pull of another atom. On the other hand, polarizing power means an atom has enough charge to cause distortion to another atom's electron cloud. I think it doesn't necessarily mean polarizability is only related to anions, but anions don't attract their outermost electrons as strongly as cations, which causes it to be more polarizable than cations.
I think cations tend to be better at polarizing atoms than they are at being polarized, and vice versa for anions, which is why we tend to talk about cations in terms of their polarizing power and anions in terms of their polarizability. If cations have polarizability and anions have polarizing power, I'd assume it'd be pretty weak.
The term "highly polarizable" refers to highly distorted electrons. With electrons more drawn to the other bonded atom, an ionic bond with more covalent character is formed. "High polarizing power" refers to the ions that cause large distortions. They are very similar concepts, but refer to different pieces of the whole process.
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