The arc followed by Bucky Barnes is broadly the same in both comics and films, a friend of Steve Rogers' who fought alongside Captain America in WW2. He was presumed dead at the war's end but returned to Cap's modern-day life as the brainwashed assassin the Winter Soldier.
Bucky's story may have a broadly comic accurate trajectory, but as with any adaptation, there are some differences in translation. Let's look more specifically at which parts of Bucky's story the MCU faithfully adapted, and which parts were changed or excluded.
10 Accurate: Cap Fails To Save Him
When Captain America was reintroduced in The Avengers issue #4, it was revealed Bucky had seemingly perished in the same event that caused Cap to be trapped in cryogenic stasis for many years. In the last days of WW2, when Cap & Bucky were tracking the theft of an experimental drone plane by Baron Zemo, the pair arrived just in time for him to launch it. Leaping aboard, they discovered too late that the plane was rigged to explode, and Bucky was unable to let go in time.
A similar fate befell his MCU counterpart. During a mission to capture Arnim Zola aboard a train, an explosion blew a hole in the train's side and left Bucky clinging to the loose railing. Cap was unable to rescue his friend in time before the railing broke loose. Despite the different circumstances, the fundamental remains the same in both tellings; Cap was unable to save his friend.
9 Inaccurate: Childhood Friendship With Steve
The beginning of Steve and Bucky's relationship is vastly different in comics and film. In the former, they first met after Steve had already become Captain America. The orphaned, military brat teen James Buchanan Barnes drafted to be Cap's sidekick (i.e. to perform more unsavory operations Cap himself couldn't be seen doing).
In the MCU, the two are instead childhood friends whose relationship goes back to well before Steve became a super-soldier; the MCU Bucky is actually a year older than Steve.
8 Accurate: The Winter Soldier
Prior to Ed Brubaker's run on Captain America, the thought of bringing Bucky back was unthinkable, but the result turned into one of the most acclaimed stories ever published in the series. In The Winter Soldier storyline, it was revealed Bucky hadn't perished in the explosion, though he had lost his right arm. Falling into the freezing waters below and soon found by a Soviet submarine, an amnesiac Bucky was brainwashed into a Soviet assassin, complete with a new cybernetic arm.
The second Captain America MCU outing, also subtitled after Bucky's assassin persona, took expected liberties with Brubaker's storyline. Bucky's arc was much the same, and the MCU Winter Soldier costume looked as if it was ripped straight out of Steve Epting's original art.
7 Inaccurate: HYDRA Creation
In the comics, the Winter Soldier was a creation of the Soviet Union. Specifically, he was the pet project of Colonel Vasily Karpov, who had a grudge against Captain America. Meant to infiltrate America more easily than other Soviet operatives, by virtue being American, Bucky was put on seemingly permanent ice after the USSR's fall.
However, he was eventually revived by Karpov's protégé, Aleksander Lukin, and it was Lukin's machinations that revealed Bucky's survival to Cap. In the MCU, however, the Winter Soldier was a creation of HYDRA, with seemingly no ties to the USSR government.
6 Accurate: Based In Russia
While the MCU Winter Soldier lacks the explicit connection to the Soviet Union of his comics counterpart, the red star emblazoned on his bionic arm and him speaking Russian in Captain America: The Winter Soldier hinted he still had some connection to Russia.
Sure enough, Captain America: Civil War would reveal that Bucky was primarily held in Siberia while under HYDRA's control, with the MCU incarnation of Vasily Karpov (reimagined as a HYDRA agent rather than a USSR patriot) being his handler.
5 Inaccurate: No Relationship With Black Widow
Bucky's most long-running romantic relationship is with Natalia Romanova, aka the Black Widow. One of Widow's combat instructors during her tutelage at the USSR's Red Room program, the pair had a brief love affair before their handlers discovered this and put an end to it. When Bucky's memories were restored in present day, he and the Widow resumed their relationship.
In the MCU, this past between Bucky and Black Widow seemingly doesn't exist; Widow only recognizes the Winter Soldier through rumors she's heard, and Bucky never shows any familiarity with her. Plus, given Widow's fate in Avengers: Endgame, the odds of a relationship between the two in the future is approximately zero.
4 Accurate: Partnership With Falcon
After Steve's (temporary) death, Bucky took his place as Captain America and struck up a friendship with Steve's frequent partner, Sam Wilson/The Falcon. The two worked together to bring the Red Skull, the mastermind behind Steve's death, to justice, and Sam would assuage Bucky's concerns he wasn't worthy to carry Cap's mantle.
Writers of the MCU seem keen to adapt this friendship. After the pair shared a rocky introduction in Civil War, they'll be teaming up in the fittingly titled The Falcon & The Winter Soldier, though this time, Sam will be carrying Cap's shield.
3 Inaccurate: Killed Stark's Parents
The Winter Soldier performed many clandestine assassinations at the behest of his handlers in both comic and cinematic continuities, but the MCU added one that didn't transpire in the comics.
In the MCU, it was Bucky who killed Howard & Maria Stark, parents of one future Iron Man. In the comics, Tony Stark's parents died in a car crash. Though foul play had occasionally been suspected, the Winter Soldier has never been linked to the deaths in the way his MCU counterpart was.
2 Accurate: "Who The Hell Is Bucky?"
There are few things more striking for a comic fan than when a film recreates a moment from the source material, panel for panel, beat for beat. Captain America: The Winter Soldier has one of those moments, and it's a crucial moment for both Bucky himself and Cap in both versions.
In both versions, when Steve sees the Winter Soldier face-to-face for the first time, he recognizes his old friend and calls him by name. The Winter Soldier only replies, "Who the hell is Bucky?": a shocking moment that only raises further questions about how the Winter Soldier came to be.
1 Inaccurate: Doesn't Become Captain America
In Issue #25 of Brubaker's run, Steve is killed at the behest of the Red Skull, but he leaves behind a letter for Tony Stark, instructing his friend that he wants Bucky to succeed him as Captain America.
Shocked, Bucky reluctantly agrees and assumes Steve's shield, even staying in the role for a while after Steve returns to life. In the MCU, Steve instead chose Sam Wilson as his successor, though without any hard feelings on Bucky's part.