The words aloud, allowed sound the same but have different meanings and spellings. Why do aloud, allowed sound the same even though they are completely different words?
The answer is simple: aloud, allowed are homophones of the English language.
Simple past tense and past participle of allow.
With use of the voice; orally: Read this passage aloud.
In a loud tone; loudly: crying aloud for help.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, from The American Heritage® Dictionary of the English Language, 4th Edition 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").