The words plait, plate sound the same but have different meanings and spellings. Why do plait, plate sound the same even though they are completely different words?
The answer is simple: plait, plate are homophones of the English language.
A braid, especially of hair.
A pleat.
To braid.
To pleat.
A smooth, flat, relatively thin, rigid body of uniform thickness.
A sheet of hammered, rolled, or cast metal.
A very thin applied or deposited coat of metal.
A flat piece of metal forming part of a machine: a boiler plate.
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").