An excerpt from 's definition for :
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In short, means fist, while means more specifically a _tightly clenched_ fist. This should come as no surprise to you, as you've already looked it up in dictionaries which say so.
It's true that it literally means "iron fist", but it isn't generally used for its literal meaning. Instead, it's figurative: when you tightly clench your fist, it's strong and unyielding like a fist of iron.