The Grey Havens sections of the film and book are, as ever, similar only in tone and meaning, rather than in actual events. The difference in actual events is maybe more pronounced than normal here, though, as many of the events (Scouring of the Shire) discussed in the book chapter do not even occur in the film.

The aftermath – book
The book chapter starts with the cleaning-up of he Shire after the Scouring of the Shire by Saruman and his troops. Frodo releases the prisoners from the lockholes in Michel Delving – including the newly slim-line Fredegar Bolger, Will Whitfoot and now old Lobelia Sackville-Baggins. After Lobelia leaves the cells, she moves back to her own people, the Bracegirdles of Hardbottle, dies shortly after, and leaves all her money to Frodo to use to help the poor and disadvantaged of the Shire..

The hobbits of the Shire then all get busy tearing down the new Shirriff-houses, and anything else that had been built by Sharkey’s men. The Hill and Bag End were cleared and Bagshot Row restored. A new row of holes were built, and with typical Shire originality, New Row.
But above all, a picture is painted of Shire life returning to normal after the ills and evils of the war and of occupation: “The fruit was so plentiful that young hobbits very nearly bathed in strawberries and cream; and later they sat on the lawns under the plum-trees and ate, until they had made piles of stones like small pyramids or the heaped skulls of a conqueror, and then they moved on. And no one was ill, and everyone was pleased, except those who had to mow the grass.” [6.IX.]

So what do our four hobbits get up to back in the Shire?
– Frodo takes up the temporary position of Deputy Mayor, as after his imprisonment, Will Whitfoot is, for a while, unfit to take up his duties. Merry and Pippin busied themselves hunting down the last ruffians.
Every now and then, known only to Sam if at all, Frodo became pained: “One evening Sam came into the study and found his master looking very strange. He was very pale and his eyes seemed to see things far away.
“What’s the matter, Mr. Frodo?” said Sam.
“I am wounded,” he answered, “wounded; it will never really heal.”” [6.IX.]

– Merry and Pippin go to live together at Crickhollow, and become famous in the Shire, being called “lordly” by all their friends and admirers: “it warmed all hearts to see them go riding by with their mail-shirts so bright and their shields so splendid, laughing and singing songs of far away.” [6.IX.]

– Sam remembers the box that Galadriel had given him and goes around all the places in the Shire where trees have been destroyed, planting saplings and putting a grain of the dust from the box at the root of each one. The remnants of the dust he cast into the air at the Three-Farthing Stone. The small silver seed, he plants in the Party Field, where the Party Tree had once stood.
The seed grows up to be a mallorn – the only one west of the Mountains and east of the Sea. It becomes of the finest mallorn trees in the world.
Sam also marries Rosie – the first event seen from this chapter in the film. The two of them move in with Frodo, who had by then resigned his office of Deputy Mayor and spent all his time writing and going through all his notes.
Elanor was then born, and when she was nearly six months old, Frodo called Sam into his study, to ask if Rose would let him travel with Frodo for a fortnight or so. He then gave Sam his diary, a book that started as Bilbo’s and then continued as Frodo’s.
“”Why, you have nearly finished it, Mr Frodo!” Sam exclaimed. “Well, you have kept at it, I must say.”
“I have quite finished, Sam,” said Frodo. “The last pages are for you.”” [6.09.]

The Aftermath – Film
The aftermath scenes in the film are drastically different to those in the book. Not only is every mention of the events in the Scouring of the Shire deleted, but the main two scenes are created just for the film – the four hobbits in the Green Dragon Inn, and Sam’s wedding.
The hobbits are first seen in the Green Dragon Inn, sitting at a table, and drinking ale. They look about them, at the simple folk and their simple lives, none of whom have any conception of the dangers they all went through to save the world, and the Shire. The four Hobbits look at each other, and raise their mugs to friends made and lost, battles won, and quests fulfilled.
Sam looks up, and sees Rosie behind the counter, and goes over to speak to her, to the great amusement of the other Hobbits.

The next – short – scene is Sam and Rosie’s wedding day. Pippin catches Rosie’s bouquet.

But after that, the film picks up the melancholic feel of the book:
Frodo: (v.o.) “How do you pick up the threads of an old life? How do you go on, when in your heart you begin to understand, there is no going back? There are some things that time cannot mend, some hurts that go too deep…that have taken hold.” [6.09.]
When it is four years to the day that they were attacked at Weathertop, Sam sees Frodo’s unfinished book in Bag End, and Frodo says that there is space for a another story after his own and Bilbo‘s contributions.

The Journey – book
Sam and Frodo set out from the Shire on September 21st, Frodo riding his horse Strider, and Sam riding his old favourite, Bill the Pony. Towards the edge of the Shire, they come across a party of Elves travelling to the Grey Havens from Imladris – Gildor, Elrond, Galadriel and many other of the high-elven folk – riding along with a sleepy Bilbo.
Tolkien then gives us a beautiful description Elrond and Galadriel: “Elrond wore a mantle of grey and had a star upon his forehead, and a silver harp was in his hand, and upon his finger was a ring of gold with a great blue stone, Vilya, mightiest of the Three. But Galadriel sat upon a white palfrey and was robed all in glimmering white, like clouds about the Moon; for she herself seemed to shine with a soft light. On her finger was Nenya, the ring wrought of mithril, that bore a single white stone flickering like a frosty star. Riding slowly behind on a small grey pony, and seeming to nod in his sleep, was Bilbo himself.” [6.IX.]

In the book, the fact that all the Ring-bearers are gathering is made clear from the start: “Then Bilbo woke up and opened his eyes. “Hullo, Frodo!” he said. “Well, I have passed the Old Took today! So that’s settled. And now I think I am quite ready to go on another journey. Are you coming?”
“Yes I am coming,” said Frodo. “The Ring-bearers should go together.”” [6.IX.]

Sam finds Frodo’s decision to leave Middle-earth hard to understand, and Frodo has to explain that he now realises that he has been too deeply hurt to be able to stay in the Shire and grow old there happily, as he knows Sam will be able to do.

The Journey – film
Even the journey to the Grey Havens occurs differently in the film. Gandalf first appears in the Shire, driving a wagon that contains an old and wrinkled Bilbo. On the journey, Bilbo talks sleepily to Frodo, as in the film, but also asks about the Ring:
Bilbo: Tell me again, lad, where are we going?
Frodo: To the harbour, Bilbo. The Elves have accorded you a special honour, a place on the last ship to leave Middle-earth.
Bilbo: Frodo, any chance of seeing that old Ring of mine again? Hmm? The one I gave you.
Frodo: I’m sorry, Uncle. I’m afraid I lost it.
Bilbo: Oh. Pity? I should like to have held it one last time.
(Frodo smiles slightly, and the two rest their heads against each other and close their eyes.)

I find this mention of the Ring somewhat strange. It isn’t very necessary, really. Firstly, saying that the elves have accorded him a special honour is a dubious telling of Tolkien’s words, as is saying that this is the last ship to the Middle-earth, when it is clear in the book that other ships follow. I also find it slightly strange that Bilbo would not know what had happened to the Ring in any way, or felt its destruction, but whether he would have done or not, I feel that this quick mention cheapens the emotion of this scene – bringing back the grasping greed of the Ring-bearers for their precious into the calm serenity of the elves’ final journey to the Havens.

The Grey Havens – book
Cirdan met the party at the gates of the Haven, and led them to the docks, where a white ship was lying, and beside it was Gandalf, standing next to Shadowfax. He openly wore Narya.
Just as Sam stood there on the docks, thinking that would have to ride home alone, in sorrow, Merry and Pippin came riding up, determined to say farewell to Frodo.

Gandalf has the last words at the Havens: “”Well, here at last, dear friends, on the shores of the Sea comes the end of our fellowship in Middle-earth. Go in peace! I will not say: do not weep; for not all tears are an evil.”
Then Frodo kissed Merry and Pippin, and last of all Sam, and went aboard; and the sails were drawn up, and the wind blew, and slowly the ship slipped away down the long grey firth.
Sam, Merry and Pippin stood watching as day turned to evening, and then night, all silent.” [6.IX.]

The Grey Havens – film
In the film, the wagon was greeted by Galadriel, Celeborn and Elrond, with another elf lurking in the background presumed to be Cirdan.
The outfits of the elves were just about similar to those described by Tolkien. Elrond is wearing grey robes with silver tracery around the sleeves, a circlet on his head. Vilya is not seen. Galadriel is wearing white, but not glimmering white, more like a hooded homespun woollen cream-white robe. Nenya is not seen. She too has a circlet on her head (as does Celeborn). Gandalf is robed in white, as per the books.
Gildor is not mentioned.

Elrond leads Bilbo onto the waiting white ship, Galadriel sends the hobbit a mischievous smile and then also embarks with Celeborn. Gandalf takes his leave with a line imported directly from the book:
Gandalf: “I will not say, “Do not weep”, for not all tears are an evil.” [6.IX.]

He then calls to Frodo to join him in boarding the ship:
Sam: What does he mean?
Frodo: We set out to save the Shire, Sam. And it has been saved. But not for me.
Sam: You don’t mean that. You can’t leave.
Frodo: (Gives Sam the Red Book.) The last pages are for you, Sam.

Frodo embraces Merry, then Pippin, then Sam, and then walks slowly onto the ship. As the ship sails, Merry and Pippin turn away, but Sam watches until it disappears.

“Well I’m home”

The last part of the book and the film concerns Sam’s return to the Shire – to his family, Rosie and Elanor, and his normal, humble life. Merry and Pippin’s return to Buckland is also mentioned.
Even Peter Jackson couldn’t make this small section radically different. Though he does manage to give Sam and Rosie two children – Elanor and an infant boy.