The words creak, creek sound the same but have different meanings and spellings. Why do creak, creek sound the same even though they are completely different words?
The answer is simple: creak, creek are homophones of the English language.
To make a grating or squeaking sound.
To move with a creaking sound.
A grating or squeaking sound.
A small stream, often a shallow or intermittent tributary to a river. Also called regionally branch, brook1, kill2, run.
A channel or stream running through a salt marsh: tidal creeks teeming with shore wildlife.
Chiefly British A small inlet in a shoreline, extending farther inland than a cove.
up the creek (without a paddle) Informal In a difficult, unfortunate, or inextricable position.
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").