The words dyeing, dying sound the same but have different meanings and spellings. Why do dyeing, dying sound the same even though they are completely different words?
The answer is simple: dyeing, dying are homophones of the English language.
Present participle of dye.
Present participle of die1.
About to die: dying patients.
Drawing to an end; declining: in the dying hours of the legislative session.
Done or uttered just before death: a dying request.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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.