The words airing, erring sound the same but have different meanings and spellings. Why do airing, erring sound the same even though they are completely different words?
The answer is simple: airing, erring are homophones of the English language.
Exposure to air for freshening or drying.
Exposure to open air for exercise or the promotion of health.
Exposure to public attention.
A radio or television broadcast.
capable of making an error.
Present participle of <xref>er</xref>.
Present participle of <xref>err</xref>.
capable of making an error
Definitions from The American Heritage® Dictionary of the English Language, 5th Edition., from the GNU version of the Collaborative International Dictionary of English., from Wiktionary, Creative Commons Attribution/Share-Alike License., from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved. 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").