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A pig's home and an eyelid's grudge share one tiny, swollen name.

means Either a muddy pen where pigs are kept, or a red, painful lump on the edge of your eyelid.

from The pig pen traces to Old English 'stig,' an enclosure; the eyelid bump comes from 'styan,' meaning to rise or swell, later mangled into 'sty.'

Two rootsPig sty and eye sty are unrelated words.
Medical nameThe eyelid version is a hordeolum, a blocked gland.
Stye tooSpelled 'stye' only for the eye, never the pig.
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