The words grade, grayed sound the same but have different meanings and spellings. Why do grade, grayed sound the same even though they are completely different words?
The answer is simple: grade, grayed are homophones of the English language.
A stage or degree in a process.
A position in a scale of size, quality, or intensity: a poor grade of lumber.
An accepted level or standard.
A set of persons or things all falling in the same specified limits; a class.
Simple past tense and past participle of gray.
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").