The words beer, bier sound the same but have different meanings and spellings. Why do beer, bier sound the same even though they are completely different words?
The answer is simple: beer, bier are homophones of the English language.
A fermented alcoholic beverage brewed from malt and flavored with hops.
A fermented beverage brewed by traditional methods that is then dealcoholized so that the finished product contains no more than 0.5 percent alcohol.
A carbonated beverage produced by a method in which the fermentation process is either circumvented or altered, resulting in a finished product having an alcohol content of no more than 0.01 percent.
A beverage made from extracts of roots and plants: birch beer.
A stand on which a corpse or a coffin containing a corpse is placed before burial.
A coffin along with its stand: followed the bier to the cemetery.
A stand on which a corpse or a coffin containing a corpse is placed before burial.
A coffin along with its stand: followed the bier to the cemetery.
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").