Final Fantasy Last Order
There are several points in Final Fantasy: Last Order that differ greatly from the points in the Final Fantasy VII game. Since Last Order only seeks to provide more details regarding the Sephiroth incident, set about five years before the events of Final Fantasy VII (as already written about in the game), this section will only deal with the areas that contradicted the points in the game, or talked about areas that were not mentioned in FF7.
Last Order
The short OAV (original anime video) deals with Zack and Cloud's escape from Shinra, after they were captured after the Sephiroth incident, and injected with Jenova cells. The OAV deals mainly with Zack rather than Cloud, who was still suffering the effects of the Jenova injections. As mentioned already in the game, it is Zack who saves Cloud and brings him out of Shinra, beating up the Shinra soldiers along the way. Zack flags down a ride to Midgar, where Zack hopes they could run a mercenary business together. A sniper howvever, had his sights set on Cloud, but Zack throws himself in front of his friend, fatally wounding himself and urging Cloud to run away.
Some flashbacks regarding Nibelheim occur, where Sephiroth burns the village down and where he attempts to take Jenova's head with him. Zack tries to stop him but is injured, and Cloud manages to wound Sephiroth severely while Sephiroth was focused on Jenova. Sephiroth injures Cloud as well, then jumps into the Mako stream carrying Jenova with him. Cloud and Zack are taken by Shinra, where Hojo hopes to experiment on them with Jenova cells.
the Turks
Tseng is in charge of the manhunt for Zack and Cloud in the series, and he more often than not feels sympathy for the two fugitives; he thinks that if Sephiroth had never existed, they wouldn't be in this predicament. Oddly enough, there are also far more Turks than is known about in the game; there are about nine Turks that appear in Last Order (including Hojo and Tseng). While Reno, Rude, Tseng, Hojo, and Elena are easily discernible, the others are not mentioned by name. It is probably safe to say that the woman with the reddish brown hair was Scarlett, and that the dark-haired man she's been annoying was Reeves, ventriloquist for FF7 team member Cait Sith. The other two men - a large burly guy, and another dark-haired guy with the weirdest hair - is still unknown.
Vincent Valentine was once a Turk, but it is unlikely he was one of the Turks seen in the anime, since according to the FF7 game timeline, he had already been experimented on and shut away in the coffin in Nibelheim, many years before Sephiroth, Zack and Cloud arrived there. The same goes for Lucrezia, who had taken sanctuary by a waterfall shortly before. None of the unaccounted male Turks could be the Turks Palmer or Heidegger either, since their FF7 pictures depict them as old men.
Also, the only people considered "Turks" were Elena, Reno, Rude and Tseng. Scarlett, Reeves, Palmer and Heidegger were actually their superiors during the FF7 game.
Zack
Until Last Order was created, there was very little known about Zack. People who played the FF7 game knew that he was responsible for saving Cloud's life, and that he was Aeris' boyfriend. They also knew that he died protecting Cloud, and that Cloud later on, his mind damaged by the experiments on him, believed himself to have lived as Zack, and took his memories and fighting style. In a sense, Zack and Cloud at one point where almost the same person.
In the anime, Zack was every bit as strong as Cloud would eventually show himself to be, taking down soldiers and avoiding bullets and helicopter chases effortlessly. His penchant for riding motorcycles seem to have carried on even today in some fragment of Cloud's memory.
What wasn't mentioned in the game was how exactly did Zack die protecting Cloud, and it was answered in Last Order. Zack, thinking he'd lost the Shinra after then, hitched a ride on a truck going into Midgar, deciding that he and Cloud should set up their own business there as mercenaries for hire / jack of all trades. Unknown to them, a sniper had been watching them as they neared Midgar. Ignoring Tseng's orders to take them alive if necessary, the sniper fired. Zack, realizing a heartbeat before of the danger, instinctively dove in front of Cloud, taking the bullet intended for the FF7 protagonist.
The anime ends abruptly after that, but it can be assumed that the truck is destroyed / overturned, and both Zack and Cloud left for dead. Cloud survives though, and takes Zack's buster sword, thinking that he is Zack.
In the Advent Children movie, there is a very worn and dilapidated buster sword driven onto the ground near the outskirts of Midgar. This is probably where Zack's grave is marked by Cloud after he regains his memories. A wolf appears from time to time around the area as well; this is probably Zack's spirit.
Sephiroth
In the game, Zack and Cloud encounters Tifa Lockhart by her dead father's body. She screams for revenge, takes the bloody sword left behind by Sephiroth and runs towards the Jenova chamber where Sephiroth was. In the OAV, Tifa doesn't wait for Cloud and Zack; she rushes in immediately and is just as immediately beaten by Sephiroth.
In the game, Sephiroth runs a sword through Zack, though it isn't enough to kill him. In the OAV, Sephiroth injures Zack and flings him onto a metal wall, leaving him near-unconscious. Everything else is the same as the game, except according to the game, Cloud knocks Sephiroth into the Lifestream. In the OAV, Sephiroth willingly jumps into the Lifestream, cradling Jenova in his arms, a smile on his face.