Like all Pokemon Games that are released in pairs, there is exclusive content for each given game that isn't found in the other version. This mainly includes Pokemon; however, there are many there aspects that differ between these two games. This means, most simply, that certain things happening differently in both games.
Exclusive Pokemon
Exclusive Pokemon to Sun: Alolan Vulpix, Alolan Ninetales, Cranidos, Rampardos, Tirtouga, Carracosta, Cottonee, Whimsicott, Rufflet, Braviary, Passimian, Turtonator, Solgaleo, Buzzwole, Kartana
Exclusive Pokemon to Moon: Alolan Sandshrew, Alolan Sandslash, Shieldon, Bastiodon, Archen, Archeops, Petilil, Lilligant, Vullaby, Mandibuzz, Oranguru, Drampa, Lunala, Pheromosa, Celesteela
Time Difference
Time In Pokemon Sun: The time clock in Pokemon Sun runs on the actual time on your 3DS. If it's daylight where you live in the real world, and your 3DS is set at the appropriate time, then it will be daylight in your Pokemon Sun Game.
Time In Pokemon Moon: The time clock in Pokemon Moon is actually opposite of the actual time on your 3DS, being 12 hours ahead. If it's daylight where you live in the real world, it will be night time in Pokemon Moon.
First Trial Totem Pokemon
First Totem Pokemon of Sun: The first Totem Pokemon you will face in Verdant Cavern will be Gumshoos.
First Totem Pokemon of Moon: The first Totem Pokemon you will face in Verdant Cavern will be Alolan Raticate.
Cover Legendary / Storyline
Story of Sun: The Story of Pokemon Sun will ultimately revolve around Cosmog eventually evolving into the Cover Legend Solgaleo.
Story of Moon: The Story of Pokemon Moon will ultimately revolve around Cosmog eventually evolving into the Cover Legend Lunala.
Exclusive Trainer Clothing
Clothing In Sun: Certain outfits are exclusive to Sun compaRed to Moon, as well as the main colors of Red, Yellow, Orange and Beige. (Opposite clothing can be purchased through Festival Plaza when you encounter players wearing them.)
Clothing In Moon: Certain outfits are exclusive to Moon compared to Sun, as well as the main colors of Green-Blue, Navy-Blue, Purple and Gray. (Opposite clothing can be purchased through Festival Plaza when you encounter players wearing them.)
Battle Trail Captain of Sun: After defeating the Fire Trial, you have the ability to battle Kiawe later on in his house.
Battle Trail Captain of Moon: After defeating the Grass Trial, you have the ability to battle Mallow later on in Lush Jungle.
Festival Plaza
Shops Exclusive to Sun: Two-Star General Store, Four-Star General Store, Soft Drink Parlor, Pharmacy, Clink-Clunk Land, Stomp-Stomp House, Rare Kitchen, Friendship Parlor, Team Red, Team Green, Team Orange, Team Purple.
Shops Exclusive to Moon: Three-Star General Store, Five-Star General Store, Ball Shop, Thump-Bump Park, Stomp-Stomp House (Different Levels), Rare Kitchen (Different Levels), Friendship Cafe, Team Yellow, Team Blue, Team Navy Blue, Team Pink.
Battle Tree Special Trainers
Special Trainers of Sun: Plumeria, Sina, Kiawe.
Special Trainers of Moon: Guzma, Dexio, Mallow