The obvious difference is that of Time. Pokemon Moon and Sun have a 12 hour difference. If you're playing during day time in Moon, it will be night in the game and vice versa. This is absent in Pokemon Sun.
As mentioned previously by Espeon, the Totem is also different (Gumshoos in Sun, Alolan Raticate in Moon)
Mascot Pokemon are different too, so the story sees a slight change, with Solgaleo in Sun and Lunala in Moon.
There is also a slight change in clothing.
>Sun has the colours Red, Yellow, Orange, Pink & Beige while Moon has the colours Green Blue, Navy Blue, Purple & Grey.
You battle the Trial Captain Kiawe (Fire Type) in Sun, and Trial Captain Mallow (Grass type) in Moon. These battles can't be fought in the opposite games, meaning you can't battle Kiawe in Moon and so on.
There are some minor differences in the latter stages of the Festival Plaza but these can be obtained by a Friend who has the other game.
In the Battle Tree, you can fight Plumeria, Sina, and Kiawe in Sun, whereas in Moon, you battle with Guzma, Dexio and Mallow. These battles are exclusive.
Finally the Pokemon you get are also differemt, with some Pokemon being exclusive to Sun, and others to Moon.
That covers about all the differences.