The words rough, ruff sound the same but have different meanings and spellings. Why do rough, ruff sound the same even though they are completely different words?
The answer is simple: rough, ruff are homophones of the English language.
Having a surface marked by irregularities, protuberances, or ridges; not smooth.
Coarse or shaggy to the touch: a rough scratchy blanket.
Difficult to travel over or through: the rough terrain of the highlands.
Characterized by violent motion; turbulent: rough waters.
A stiffly starched frilled or pleated circular collar of lace, muslin, or other fine fabric, worn by men and women in the 16th and 17th centuries.
A distinctive collarlike projection around the neck, as of feathers on a bird or of fur on a mammal.
A Eurasian sandpiper (Philomachus pugnax) the male of which has collarlike, erectile feathers around the neck during the breeding season.
The playing of a trump card when one cannot follow suit.
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.