The words braking, breaking sound the same but have different meanings and spellings. Why do braking, breaking sound the same even though they are completely different words?
The answer is simple: braking, breaking are homophones of the English language.
Present participle of brake.
The change of a simple vowel to a diphthong, especially in various Germanic languages, often caused by the influence of neighboring consonants.
A form of urban dance involving styles such as rocking, popping, and b-boying, usually performed to funk. Also called break dancing.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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").