The words boulder, bolder sound the same but have different meanings and spellings. Why do boulder, bolder sound the same even though they are completely different words?
The answer is simple: boulder, bolder are homophones of the English language.
comparative form of bold: more bold
A large rounded mass of rock lying on the surface of the ground or embedded in the soil.
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").