A quick scan of about 20 on-line 'dictionaries' reveals some variance in the definition. Oxford (US english vers.) allows applying "homonym" to words that are -- and are NOT (their example: "meet/meat right/write/rite") -- spelled the same, so long as they are homophones.
http://oxforddictionaries.com/definition/homonym?region=us

English being what it is, JavaFan's advice (++) to check with a linguistics forum seems well taken.

In reply to Re^2: Wishlist: help for people that don't differentiate homonyms by ww
in thread Wishlist: help for people that don't differentiate homonyms by Anonymous Monk

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