The words gaff, gaffe sound the same but have different meanings and spellings. Why do gaff, gaffe sound the same even though they are completely different words?
The answer is simple: gaff, gaffe are homophones of the English language.
A large iron hook attached to a pole or handle and used to land large fish.
Nautical A spar attached to the mast and used to extend the upper edge of a fore-and-aft sail.
A sharp metal spur or spike fastened to the leg of a gamecock.
A climbing hook used by telephone and electric line workers.
A clumsy social error; a faux pas: "The excursion had in his eyes been a monstrous gaffe, a breach of sensibility and good taste” ( Mary McCarthy).
A blatant mistake or misjudgment.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").