The words aired, erred sound the same but have different meanings and spellings. Why do aired, erred sound the same even though they are completely different words?
The answer is simple: aired, erred are homophones of the English language.
abounding in fresh air.
made public by radio or television.
Simple past tense and past participle of <xref>air</xref>.
open to or abounding in fresh air
Simple past tense and past participle of <xref>er</xref>.
Simple past tense and past participle of <xref>err</xref>.
Definitions 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").