The words roomer, rumor sound the same but have different meanings and spellings. Why do roomer, rumor sound the same even though they are completely different words?
The answer is simple: roomer, rumor are homophones of the English language.
One who rents a room or rooms in which to live; a lodger.
A piece of unverified information of uncertain origin usually spread by word of mouth.
Unverified information received from another; hearsay.
To spread or tell by rumor.
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").