The words chord, cord, cored sound the same but have different meanings and spellings. Why do chord, cord, cored sound the same even though they are completely different words?
The answer is simple: chord, cord, cored are homophones of the English language.
Music A combination of three or more pitches sounded simultaneously.
Harmony, as of color.
To be in accord; agree.
Music To play chords on an instrument.
A slender length of flexible material usually made of twisted strands or fibers and used to bind, tie, connect, or support.
An insulated flexible electric wire fitted with a plug or plugs.
A hangman's rope.
An influence, feeling, or force that binds or restrains; a bond or tie.
Simple past tense and past participle of core.
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").