The words mode, mowed sound the same but have different meanings and spellings. Why do mode, mowed sound the same even though they are completely different words?
The answer is simple: mode, mowed are homophones of the English language.
A manner, way, or method of doing or acting: modern modes of travel. See Synonyms at method.
A particular form, variety, or manner: a mode of expression.
A given condition of functioning; a status: The spacecraft was in its recovery mode.
The current or customary fashion or style. See Synonyms at fashion.
Simple past tense and past participle of mow.
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").