The words phosphorous, phosphorus sound the same but have different meanings and spellings. Why do phosphorous, phosphorus sound the same even though they are completely different words?
The answer is simple: phosphorous, phosphorus are homophones of the English language.
Of, relating to, or containing phosphorus, especially with valence 3 or a valence lower than that of a comparable phosphoric compound.
A highly reactive, poisonous, nonmetallic element occurring naturally in phosphates, especially apatite, and existing in three allotropic forms, white (or sometimes yellow), red, and black. An essential constituent of protoplasm, it is used in safety matches, pyrotechnics, incendiary shells, and fertilizers and to protect metal surfaces from corrosion. Atomic number 15; atomic weight 30.9738; melting point (white) 44.1°C; boiling point 280°C; specific gravity (white) 1.82; valence 3, 5. See Table at element.
A phosphorescent substance.
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").