The words brake, break sound the same but have different meanings and spellings. Why do brake, break sound the same even though they are completely different words?
The answer is simple: brake, break are homophones of the English language.
A device for slowing or stopping motion, as of a vehicle, especially by contact friction.
Something that slows or stops action.
To reduce the speed of with or as if with a brake.
To operate or apply a brake.
break in To intrude.
A violation: a security break.
To become cracked or split.
To cause to separate into pieces suddenly or violently; smash.
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").