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.
altogether
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.
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").