The words rheumy, roomie, roomy sound the same but have different meanings and spellings. Why do rheumy, roomie, roomy sound the same even though they are completely different words?
The answer is simple: rheumy, roomie, roomy are homophones of the English language.
of, relating to, or producing rheum from the mucous membranes; watery
Informal A roommate.
Having plenty of room; spacious. See Synonyms at spacious.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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.