The words arc, ark sound the same but have different meanings and spellings. Why do arc, ark sound the same even though they are completely different words?
The answer is simple: arc, ark are homophones of the English language.
Something shaped like a curve or arch: the vivid arc of a rainbow.
Mathematics A segment of a circle.
An electric arc.
Astronomy The apparent path of a celestial body as it rises above and falls below the horizon.
Bible The chest containing the Ten Commandments written on stone tablets, carried by the Hebrews during their desert wanderings. Also called Ark of the Covenant.
Judaism The Holy Ark.
Bible The boat built by Noah for survival during the Flood.
Nautical A large, commodious boat.
Definitions 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.
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").