The words handsome, hansom sound the same but have different meanings and spellings. Why do handsome, hansom sound the same even though they are completely different words?
The answer is simple: handsome, hansom are homophones of the English language.
Pleasing and dignified in form or appearance. See Synonyms at beautiful.
Generous or copious: a handsome reward. See Synonyms at liberal.
Marked by or requiring skill dexterity: did some handsome maneuvers on the skating rink.
Appropriate or fitting: a handsome location for the new school.
A two-wheeled covered carriage with the driver's seat above and behind. Also called hansom cab.
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.