The words ringing, wringing sound the same but have different meanings and spellings. Why do ringing, wringing sound the same even though they are completely different words?
The answer is simple: ringing, wringing are homophones of the English language.
the giving of a ring as a token of engagement
having the character of a loud deep sound; the quality of being resonant
the sound of a bell ringing
Present participle of <xref>ring</xref>.
Present participle of <xref>wring</xref>.
a wringer. See <er>Wringer</er>, 2.
a. & n. from <xref urlencoded="wring">wring</xref>, v.
Definitions from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved., from Wiktionary, Creative Commons Attribution/Share-Alike License., from the GNU version of the Collaborative International Dictionary of English. and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.