The words yay, yea sound the same but have different meanings and spellings. Why do yay, yea sound the same even though they are completely different words?
The answer is simple: yay, yea are homophones of the English language.
a branch of the Tai languages
<xref>so</xref>, <xref>this</xref> (accompanied by a hand gesture)
An expression of happiness.
Alternative form of <xref>yea</xref> (yes).
not only so, but
An <xref>affirmative</xref> <xref>vote</xref>, usually but not always spoken
Common misspelling of <xref>yeah</xref>.
Definitions from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved., 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.