The words plane, plain sound the same but have different meanings and spellings. Why do plane, plain sound the same even though they are completely different words?
The answer is simple: plane, plain are homophones of the English language.
Free from obstructions; open; clear: in plain view.
Obvious to the mind; evident: make one's intention plain. See Synonyms at apparent.
Not elaborate or complicated; simple: plain food.
Straightforward; frank or candid: plain talk.
Mathematics A surface containing all the straight lines that connect any two points on it.
A flat or level surface.
A level of development, existence, or achievement: scholarship on a high plane.
An airplane or hydroplane.
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.