The main difference is that 'ao' is a noun and 'aoi' is an adjective For example, if you are saying that you like the colour blue, you would say "watashi wa ao ga suki desu". If you were referring to something that's blue, eg a pencil, you would say "aoi enpitsu". 'Aka wain' is different because 'red wine' can be considered a noun in whole.

rechelofpie It is not a simple issue to decide the aka in aka-wain is a noun. Before I answerd this question, I thought about two possibilities. One is just that rechelofpie said, aka is a noun. Maybe many Japanese feel that this is the correct answer. But I thought that the other possibility exists. It is that aka is the root of the adjective aka-i. Then I found other adjectives that drop -i ending when it makes a complex noun. So I couldn't conclude that this aka is a noun.

I just want to add one thing. This is not a phenomena that only occurs to colors. Many other adjectives also drop "i" when they create a new word. For example: amai(sweet)+kuchi -> ama-kuchi(sweet taste), karai(spicy)+kuchi -> kara-kuchi(spicy taste), ureshii(glad)+namida(tear) -> ureshi-namida

Hi. Aiko's answer is good. I'd like to add some examples: 赤信号　(red traffic light) This is similar to the explanation that Aiko has given. 青りんご（blue apple) => OK, here, it's means actually "green apple" but green and blue are often mixed in Japan. If you say 青いりんご、then it's an apple which is "green". But if you say 青りんご、it's a particular kind of green apple (e.g. Granny Smith). But 白黒(しろくろ）テレビ（black/white TV), but it's wrong to say 白黒いテレビ。 I hope this helps a bit more :-)

I think this is a very interesting question. In my opinion, Japanese tends to omit '-i' to describe the colors of nouns when it is considered as almost one word. So, 'aka wain' is used as a noun in spite of two words. If there were various colors of wine, such as bule wine or green wine, I think 'akai wine' would be used. I hope this will help.