The words spade, spayed sound the same but have different meanings and spellings. Why do spade, spayed sound the same even though they are completely different words?
The answer is simple: spade, spayed are homophones of the English language.
A sturdy digging tool having a thick handle and a heavy, flat blade that can be pressed into the ground with the foot.
Any of various similar digging or cutting tools.
To dig or cut with a spade.
Games A black, leaf-shaped figure on certain playing cards.
Simple past tense and past participle of spay.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").