The words berg, burg sound the same but have different meanings and spellings. Why do berg, burg sound the same even though they are completely different words?
The answer is simple: berg, burg are homophones of the English language.
A mass of floating or stationary ice; an iceberg.
Informal A city or town: "There are no more opportunities for you in this burg” ( Damon Runyon).
A fortified or walled town in early or medieval Europe.
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").