Similar to the first person shooter, except this time you can see your player character. Camera angles may vary from over the shoulder to full body.
Single player adventure
Story based narratives which may involve quest missions. You play as a single player with no interaction with other players, only computer controlled characters and enemies. The Fallout series is a good example of this genre (though this can also be played in FPS mode). Most gameplay involves gun battles.
Strategy and Stealth
Many 3rd person shooters involve a level of planning, and is not just a straight run and gun situation. Instead of entering a fast paced arena all guns blazing, these games may require you to stay out of sight, use sniper rifles and knives as well as guns. Most games of this type are military based where you play as a soldier that is part of a team. Games like The Division, and Ghost Recon are examples of this type of game.
Another single player game where you have weaponry and do take part in gun battles, but the main part of the game is solving puzzles (such as opening a locked door using pressure sensitive pads) climbing, platforming and questing. The best example of this is the Tomb Raider series.
A multiplayer game where the players kill each other (or the environment does) until one is left and declared the winner. There is a mechanic that reduces the play area so that players are forced to confront each other. which differentiates this from a normal Deathmatch. First came to prominence with PUBG and made popular by Fortnite.
Game mechanics and prominent features
Most of the features of a FPS can be found in a 3rd person shooter, such as weapon swapping, limited ammo, loot drops, however there are a few mechanics that are more prominent in this genre.
Targeting enemies without seeing through the eyes of a character is normally done through some sort of aim assistance, where enemies can be tagged, or the gun will automatically fire at the nearest enemy that is in front of the player before targeting another.
Some 3rd person shooters use a first person camera in certain situations, such as aiming down a sight, flying a drone, or using binoculars.
Extensive use of HUDs and UI
Because you are not seeing out of the players eyes these games give you a bigger field of vision. However game designers tend to restrict that by adding maps, radars, interfaces and player data. 3rd person shooters tend to have more on screen info as you play, while FPS games will use full screen menus that interrupt play (though obviously there are exceptions).
Can you make these in Dreams?
Absolutely. You will need to make a gun mechanic, but the built in camera in the basic puppet model is already set up with a 3rd person camera.
Proper Battle Royale games however cannot be made as the multiplayer options only allow 4 players, and not the 100 you would need. However, you could make a version of Battle Royale with AI characters, though that is a big task as AI in Dreams is not an easy thing to build, and there are many factors to consider in creating a reasonable computer controlled Fortnite player. Or just have a 4 player Battle Royale in a smaller environment.