The words rhumb, rum sound the same but have different meanings and spellings. Why do rhumb, rum sound the same even though they are completely different words?
The answer is simple: rhumb, rum are homophones of the English language.
A rhumb line.
One of the points of the mariner's compass.
An alcoholic liquor distilled from fermented molasses or sugar cane.
Chiefly British Odd; strange.
Chiefly British Presenting danger or difficulty.
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").