Limited vs. omniscient narration
Third person narration is a literary style where the narrative is told from the perspective of a narrator who exists outside of the story in which third person pronouns (he, she, they) are used to refer to characters within the story.
Third person limited narration focuses the story on the thoughts, feelings, and experiences of a singular character. Using it successfully creates closeness between the reader and the main character (sometimes multiple characters), which can strengthen reader engagement.
Third person omniscient, on the other hand, allows the reader access to the thoughts, feelings, and experiences of multiple characters. The exterior narrator knows everything about the characters at all times, which can provide opportunities for revealing different viewpoints or information that may not have been accessible through a focal character.
The key difference
At the heart of the differences between the two narrative styles lies in how they can be used. In a limited narrative, there may be multiple viewpoint characters (just as you'd find in an omniscient narrative); however, it's pivotal that the lines between perspectives remain crisp and clear in a limited narrative. So, while each scene or chapter may be told from the perspective of a different character, the perspective will be limited within each scene or chapter to that one character. Any insertion of the thoughts, feelings, or inner life of another character within that space results in head-hopping. Omniscient narratives, however, will slide in and out of multiple character's heads (so to speak) at any given moment in the story.
Third person limited examples
Fahrenheit 451, Ray Bradbury
Bradbury focuses the perspective on Guy Montag, keeping the reader close as Guy struggles to break free of the social constraints of the fictional America in which he lives.
It was a special pleasure to see things eaten, to see things blackened and changed. With the brass nozzle in his fists, with this great python spitting its venemous kerosene upon the world, the blood pounded in his head, and his hands were the hands of some amazing conductor playing all the symphonies of blazing and burning to bring down the tatters and charcoal ruins of history . . . He wanted above all, like the old joke, to shove a marshmallow on a stick in the furnace . . . Montag grinned the fierce grin of all men singed and driven back by flame.
2. The Giver, Lois Lowry
In Lowry's dystopian YA novel, the reader follows the journey of Jonas as he becomes an apprentice to the community's Giver. The reader experiences his emotions and thoughts as he is immersed in memories long forgotten by the community.
Overwhelmed by pain, he lay there in the fearsome stench for hours, listened to the men and animals die, and learned what warfare meant. Finally, when he knew that he could bear it no longer and would welcome death himself, he opened his eyes and was once again on the bed. The Giver looked away, as if he could not bear to see what he had done to Jonas. “Forgive me,” he said.
In both examples, the reader stays close to the viewpoint characters, as though standing right behind them. We feel the heat of the flames with Guy and feel Jonas's distress as he experiences war. There are no shifts to other perspectives beyond the focal characters.
Third person omniscient examples
Dune, Frank Herbert
Because I'm listening to an audiobook of Dune right now, it had to make the list. If ever there was a firmly third person omniscient narrative, Dune is it.
Damn that Jessica! the Reverend Mother thought. If only she'd borne us a girl as she was ordered to do! Jessica stopped three paces from the chair, dropped a small curtsy, a gentle flick of left hand along the line of her skirt. Paul gave the short bow his dancing master had taught—the one used "when in doubt of another's station." The nuances of Paul's greeting were not lost on the Reverend Mother. She said: "He's a cautious one, Jessica." Jessica's hand went to Paul's shoulder, tightened there. For a heartbeat, fear pulsed through her palm. Then she had herself under control. "Thus he has been taught, Your Reverence." What does she fear? Paul wondered.
In this short passage, the POV jumps from the Reverend Mother to Jessica to Paul in the space of twelve lines.
2. The Road, Cormac McCarthy
For a slightly more contemporary example, The Road might not be an obvious choice as it follows a father (the man) and son (the boy) exclusively throughout their journey in a postapocalyptic world. McCarthy establishes early on, however, that the narrator is far removed from the main characters with knowledge of the world to which the father and son are not privy.
[The man] woke in the morning and turned over in the blanket and looked down the road through the trees the way they'd come in time to see the marchers four abreast. Dressed in clothing of every description, all wearing red scarves at their necks. Red or orange, as close to red as they could find. He put his hand on the boy's head. Shh, he said.
McCarthy is subtle. The perspective here is mainly the man's, but briefly the reader is told that the colors of the scarves worn by the marchers are "as close to red as they could find," a detail beyond the scope of the man's experience and clearly pointing to a narrator who knows beyond the time and space of the immediate story.
Can they be mixed?
Writers will need to decide early in the writing process whether they want to set up their story in third person limited or third person omniscient. For third person limited, for instance, it could be jarring for the reader to engage with a limited perspective for several chapters and then be thrust into a chapter where the perspective changes several times with no precedence. In a third person omniscient narrative, not only does the narrator know just about everything there is to know about all the characters (another aspect of omniscient narration I'm not going to dive into here is the level of omniscience) but they might also know information that none of the characters know—indeed, they have knowledge of the complete world of the story, making for increased opportunities of suspense and irony.
(That said, experienced writers can break the rules. Take J. K. Rowling's Harry Potter and the Sorcerer's Stone for example. The first chapter is written in third person omniscient [Harry hasn't even arrived on the scene yet!], while the rest of the series is written in third person limited [usually from Harry's perspective].)