The words plaiter, plater sound the same but have different meanings and spellings. Why do plaiter, plater sound the same even though they are completely different words?
The answer is simple: plaiter, plater are homophones of the English language.
One who, or that which, plaits.
someone who plates metal.
someone who installs sheet metal and armour plating, particularly on trains, ships, tanks, and similar items
A machine for calendering paper.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License 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").