The words mat, matt, matte sound the same but have different meanings and spellings. Why do mat, matt, matte sound the same even though they are completely different words?
The answer is simple: mat, matt, matte are homophones of the English language.
A flat piece of coarse fabric or other material used for wiping one's shoes or feet, or in various other forms as a floor covering.
A small flat piece of decorated material placed under a lamp, dish of food, or other object.
Sports A floor pad to protect athletes, as in wrestling or gymnastics.
A densely woven or thickly tangled mass: a mat of hair.
Alternative spelling of matte.
Variant of mat2.
Variant of mat2.
A mixture of a metal with its sulfides, produced by smelting the sulfide ores of copper, lead, or nickel.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, 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").