The words dam, damn sound the same but have different meanings and spellings. Why do dam, damn sound the same even though they are completely different words?
The answer is simple: dam, damn are homophones of the English language.
A barrier constructed across a waterway to control the flow or raise the level of water.
A body of water controlled by such a barrier.
A barrier against the passage of liquid or loose material, as a rubber sheet used in dentistry to isolate one or more teeth from the rest of the mouth.
An obstruction; a hindrance.
To pronounce an adverse judgment upon. See Synonyms at condemn.
To bring about the failure of; ruin.
To condemn as harmful, illegal, or immoral: a cleric who damned gambling and strong drink.
To condemn to everlasting punishment or a similar fate; doom.
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").