The words shire, shyer sound the same but have different meanings and spellings. Why do shire, shyer sound the same even though they are completely different words?
The answer is simple: shire, shyer are homophones of the English language.
A former administrative division of Great Britain, equivalent to a county.
A Shire horse.
An obsolete form of <internalXref urlencoded="sheer">sheer</internalXref>.
A share; a portion.
A thrower; in <em>cricket</em>, one who, in the guise of bowling, throws the ball.
<xref>comparative</xref> form of <xref>shy</xref>: more <xref>shy</xref>
Definitions from The American Heritage® Dictionary of the English Language, 5th Edition., from The Century Dictionary., 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").