The difference is a very simple one. It has nothing to do with grammar - it's purely a question of writing two words as one. The word 'another' means 'one other'. The book/the other book The books/ the other books That book/ that other book Those books/ those other books My book/my other book A book/ another book For example: 'Do you want this cake?' 'No, I want that other one (or the other one)'. but 'I ordered A Coke and drank it. But I was still thirsty, so I ordered ANOTHER one' We can't say 'a other', because 'other' begins with a vowel, and so 'a' changes to 'an'. But we don't write 'an other' as two words - we write it as one: 'another'. Easy, isn't it? There's no big mystery - it's just an+other.

"I would like the other car." This means you would like a different car than what you currently have. "I would like another car." This means you want an additional car.