The words populous, populus, populace sound the same but have different meanings and spellings. Why do populous, populus, populace sound the same even though they are completely different words?
The answer is simple: populous, populus, populace are homophones of the English language.
The general public; the masses.
Containing many people or inhabitants; having a large population.
A genus of dicotyledonous trees of the order Salicineæ, including the poplar and aspen, having diœcious flowers in catkins without floral envelops, and distinguished from Salix, the willow, by the numerous ovules, obliquely lengthened and cup-shaped disks, broad and toothed bracts, loosely flowered and generally pendulous catkins, and broad leaves.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from The Century Dictionary and Cyclopedia and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.