The words all together, altogether (2 words/1 word) sound the same but have different meanings and spellings. Why do all together, altogether (2 words/1 word) sound the same even though they are completely different words?
The answer is simple: all together, altogether (2 words/1 word) are homophones of the English language.
Entirely; completely; utterly: lost the TV picture altogether; an altogether new approach.
With all included or counted; all told: There were altogether 20 people at the dinner.
On the whole; with everything considered: Altogether, I'm sorry it happened.
A state of nudity. Often used with the: in the altogether.
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.