The words em, m sound the same but have different meanings and spellings. Why do em, m sound the same even though they are completely different words?
The answer is simple: em, m are homophones of the English language.
Printing The width of a square or nearly square piece of type, used as a unit of measure for matter set in that size of type.
The letter m.
Printing Such a measure for 12-point type; a pica.
The 13th letter of the modern English alphabet.
Any of the speech sounds represented by the letter m.
The 13th in a series.
Something shaped like the letter M.
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").