Who is Sam in the movie?
Samwise Gamgee is Frodo’s gardener and friend. He’s a friendly and loyal Hobbit, clearly not as educated or well-off as Frodo but with enough common sense to contribute to his master’s journey.

Who was Sam in the book?
Samwise Gamgee is, like his father before him, gardener at Bag End. He’s Frodo Baggins‘ servant, and a very loyal one at that. With Fredegar Bolger, Peregrin Took and Meriadoc Brandybuck he discovers the plan behind the move to Crickhollow, and later accompanies his master on the trip to Mordor.
The Gamgees live in Bagshot Row.

Changes in Fellowship of the Ring
Introductions
In the books we are introduced to Samwise Gamgee as the Gaffer’s son. We don’t actually meet him until the second chapter (1.II. The Shadow of the Past), where he’ll be defending his master against the gossips and jesters in the Green Dragon in Bywater.
He only becomes important at the end of this chapter, when Gandalf orders him to go with Frodo to Bree, which he does.

In the movies, we meet Sam at Bilbo’s birthday party where Frodo practically shoves him into Rosie Cotton’s arms. There’s also a shot of him in the Extended Edition sequence of ‘Concerning Hobbits’, as you can see here.
From the very beginning, Sam is important: he’s a friend of Frodo’s, not just a servant. This bond isn’t present in the book, it is in fact something that grows throughout the journey.

General Characteristics
Tolkien portrays Samwise Gamgee first and foremost as Frodo’s servant. This is made clear by the first lines about the hobbit: they inform the readers that after the old Gaffer got too old, his son Sam took over as gardener. ‘Both father and son were on very friendly terms with Bilbo and Frodo.’
In the movie, ‘friendly terms’ was re-interpreted as ‘friends’, and servant as caretaker. This is made to clear to us in scenes like the already mentioned birthday party and the extended scene in the Green Dragon Inn.

Tolkien made use of dialects in his portrayal of certain characters, and Sam certainly is one of them: he speaks a very common form of English, making a lot of grammatical mistakes and using a whole lot of standard expressions. He’s also the character that refers most to common sayings, or folk wisdom his father taught him.
Although Bilbo taught Sam how to read and write and he learned a lot from Bilbo’s tales, he makes a somewhat naive impression in ‘Fellowship of the Ring’. All in all, Tolkien did his very best to portray Sam as a common lad, an ‘everyman’ if you like.
This was not altered in the movie: Sean Astin speaks with a rich English accent, using the same grammar and proverbs as book Sam. His character is also portrayed as a man of ‘common sense’ rather than books and lore, and his curiosity shows in scenes like the encounter with the Elves or the hobbits’ journey with Strider.
As for appearance, Tolkien describes Sam as chubby, with curly hair.

Sam’s main characteristic is his loyalty to Frodo, and his concern for his master. This is reflected throughout the books in many ways, and it is emphasised even more in the movie version of ‘Lord of the Rings’: he panics when he looses sight of Frodo in the cornfield, he is the one who prevents Frodo from putting on the Ring when hiding from the Nazgul, he barges into the room when Strider ‘hobbitnaps’ Frodo in the Prancing Pony (and stays very suspicious of him).
Some scenes are straight from the book, like his entering the room in Rivendell or hiding in the bushes during the council (he was actually just sitting there, in a corner), but a lot was added to enhance that sense of Sam looking out for Frodo: if you freeze-frame any random scene you can see that most of the time Sam – if included in the picture – is looking at Frodo.
This makes it all the more surprising that Sam wasn’t invited to look into Galadriel’s Mirror, one of the more (most) crucial scenes for this character in book 2.

The Sam Factor
This intensified bond between Sam and Frodo goes at the expense of some other crucial relationships in the book.
First and foremost there’s of course the random appearances and disappearances of Bill the Pony. In ‘Fellowship of the Ring’, Bill is for the entire Fellowship what Shadowfax will be to Gandalf in ‘The Two Towers’ and ‘Return of the King’: the pony is a extension of Sam himself, and like Sam is a happy servant of Frodo, Bill is a happy servant of the entire Fellowship.

But it also affects the characters of Merry and Pippin, and their bond with Frodo. In the book, the band of hobbits is not immediately a foursome: there are five hobbits to begin with, and one is definitely in the centre while another is definitely not. Frodo, as in the movie, is the central figure of the group, and Sam is his servant. Of course his status is different, but he is not a friend of Frodo’s like Merry and Pippin are, or Fatty Bolger for that matter.
In the movie, Merry and Pippin tumble into the whole adventure by accident, and just keep stumbling along. In the books, both friends made a choice to accompany Frodo, twice: once in the house in Crickhollow, and again in Rivendell. This dimension of friendship in two young hobbits knowing full well what they’re getting themselves into (or as well as they can), but still determined to stay with their friend and help him, is lost in the movies.

Because of the bond between Frodo and Sam, Merry and Pippin are also shown as a ‘duo’, more than individual characters: when Frodo starts his journey he is accompanied by both Sam and Pippin (1.III.), in Bree Merry goes out on his own for a walk and encounters a Ringwraith (1.IX).

Last but certainly not least, Sam’s presence on the foreground has a certain effect on the character of Frodo also: because of Sam’s ever watchful glance and his more active role in the quest, Frodo’s own importance becomes relative. Not only is Frodo a whole different character in the movie, he is already overshadowed by the character of Sam – something that in the books doesn’t happen until the two are separated. By stressing Sam’s importance to Frodo, the character of the Ring-bearer (one of the strongest personalities in the book, with great resilience) is greatly weakened.