Neon Genesis Evangelion ran 26 episodes across 1995-1996, concluded in 1997 with The End of Evangelion, a film which both complement and supplants the final two episodes of the series. Despite ending not once but twice, the series ended up becoming an outright phenomenon and more was inevitable.
Thus, 2008 saw the release of Evangelion 1.0: You Are (Not) Alone. This film was the first chapter of a tetralogy known as Rebuild of Evangelion. The Rebuild films blur the line between remake, sequel, and meta-textual deconstruction. As such, there's plenty of differences between them and the original NGE.
10 In The Rebuilds, NERV Knows About Lilith
An ongoing subplot through Neon Genesis Evangelion was the mystery of what was hidden in the lowest levels of NERV: Central Dogma. It turned out to be an Angel, one kept in stasis with the Spear of Longinus, and who was central to both Gendo and SEELE's plans. Initially, this was believed to be the first Angel, Adam, but the 24th episode revealed it was actually Lilith, the 2nd Angel and humanity's parent.
In Rebuild, Lilith still slumbers beneath NERV, but the entire staff is aware of this fact, the Angel's true identity, and humanity's lineage. In Evangelion 1.0, Misato takes Shinji to Central Dogma to see Lilith and explains what it is so Shinji will understand what all of NERV is fighting for.
9 Kaworu Shows Up Earlier In The Rebuilds
Kaworu debuted in Evangelion Episode 24 - sent to replace Asuka as Unit-02's pilot, he and Shinji instantly hit it off and Kaworu even admitted that he loved Shinji. Unfortunately, Kaworu is actually Tabris, the 17th Angel. To save humanity, Shinji has to kill his newfound love. Despite Kaworu's brief presence in the series, he's a pivotal character - his death and Shinji's guilt over it factor greatly into both endings.
In the Rebuilds, Kaworu debuts earlier. In the last scene of 1.0, he awakens on the moon and looks to Earth, while in 2.0's post-credits scene, he descends from the Moon piloting Eva Mark.06. In both scenes, Kaworu shows awareness of Shinji, but they don't meet until 3.0.
8 Mari Illustrious Makinami Has No Counterpart In The Original Anime
Evangelion 1.0 is a condensed repackage of the NGE's first six episodes - any differences are minor and cosmetic. Starting at 2.0, the narrative starts to veer off course. The film opens with Mari Illustrious Makinami, a character with no counterpart from the original series, piloting EVA Unit-05.
After her EVA is destroyed in battle, Mari parachutes into Japan, hijacks Unit-02 to fight Zeruel, then takes Kaji's role from Episode 19 as the one who pushes Shinji to pilot Unit-01 again. Mari returns in both of the latter two Rebuild films, now the pilot of Unit-08 and Asuka's wing-woman, and ultimately ends up with Shinji in the final film. Considering that film's message that Shinji could only be happy without the burdens of the past (personified by the Evangelions themselves), its fitting that he finally found love with a character who isn't from NGE.
7 The Line-Up Of Angels Is Different
In NGE, there were 18 Angels in total - on top of Adam, Lilith, and the Lilin (i.e. humanity as a whole), there were 15 whom NERV had to directly defeat. For a 26 episode series, this as appropriately spaced out - a new Angel almost every week, but with some downtime or two-part battles here and there.
In the Rebuild films, there are only 13 Angels. Some Angels from the original series are absent, with new ones inserted in - notably a new Angel was inserted between Lilith and Sachiel, pushing the sequence's number back by one (i.e. in NGE Sachiel, the Angel Shinji first fights, is the 3rd Angel. In the Rebuilds, it's the fourth). However, even in the Rebuilds, the sequence begins with Adam and ends with Kaworu (who are technically the same being).
6 Asuka Langley Shikinami, Not Asuka Langely Soryu
Asuka Langley was the character who changed most from NGE to Rebuild of Evangelion. On one hand, she looked the same, was still the pilot of EVA Unit-02, and had mostly the same personality. However, her Japanese surname was changed from Soryu to Shikinami, and this change belied deeper differences.
During Evangelion 2.0, Asuka is sometimes shown speaking to a sock puppet doll, in contrast to the original Soryu's hatred of dolls. As revealed in Evangelion 3.0 + 1.0, this is because Shikinami has a totally different backstory from Soryu - instead of her mother committing suicide when Asuka was a toddler, Asuka Shikinami never even had parents. Instead, she is the sole surviving clone of the "Shikinami-series."
5 Asuka Pilots Unit-03, Not Toji
Another change to Asuka in Evangelion 2.0 was placing her at one of the series' pivotal moments. In NGE, Shinji's friend Toji Suzuhara is chosen to be the pilot of the newly completed EVA Unit-03. Unfortunately, the EVA is taken over by the 13th Angel, Bardiel. Shinji refuses to destroy it, so a remote-controlled Unit-01 tears apart Unit-03 before crushing the entry plug and crippling Toji. A guilt-ridden Shinji briefly resigns as a pilot afterwards.
A similar chain of events plays out in Evangelion 2.0, but Asuka is the pilot of Unit-03 instead. Asuka also remains merged with Bardiel (here the 9th Angel), necessitating that she wear an eyepatch to keep the Angel contained - in 3.0 + 1.0, she tears the patch off to evolve Unit-02 to a divine being.
4 The Fight With Zeruel Ends Much Differently
In NGE Episode 19, Shinji returns to being an EVA pilot in time to fight Zeruel - after Unit-01 loses power, it goes berserk and devours the Angel - Shinji's high sync rate leaves him temporarily merged with Unit-01 for most of the following episode. In Episode 23, Unit-00 is infected by the Angel Armisael, so Rei self-destructs her EVA to kill the Angel.
Evangelion 2.0 combines these events for its third act. Unit-00 and Rei are absorbed by Zeruel, so when Unit-01 goes berserk, it's not just to defeat the Angel, but to save Rei. While Shinji pulls her from the Angel's core, Unit-01 and Shinji's sync rate, mixed with the interface with an Angel, triggers the Third Impact.
3 After Evangelion 2.0, There Is A Time Jump
Evangelion 3.0 marks the point when the Rebuilds start to deviate from the broad outline of the original. While there is some overlap between the film and NGE (Shinji's relationships with Kaworu and the new Rei clone in particular), the narrative heads in a completely different direction. 3.0 opens 14 years after the Third Impact, with Earth outright decimated.
In the intervening years, NERV has split. NERV itself is still led by Gendo & Fuyutsuki, and still ostensibly aligned with SEELE's agenda (though Gendo takes the group off the table by the film's end). Meanwhile, breakaways led by Misato and including Asuka, Mari, and Ritsuko, have formed WILLE, a group dedicated to opposing NERV's plans for a Final Impact.
2 Kaji Dies Differently In The Rebuilds
Many of the series' supporting characters were absent from Evangelion 3.0, among them Ryoji Kaji. 3.0 + 1.0 reveals that this is because he died in the Third Impact, which helps explain why Misato was so angry with Shinji in the previous film. However, it turns out that Misato was pregnant when her lover died - she gave birth to a son named for his father, even though she couldn't bear to raise him personally.
This is quite a different fate for Kaji compared to NGE - after having played his luck against many powerful factions, he's ultimately assassinated by an unseen gunman. The only parting gift NGE Misato gets is a regretful voicemail.
1 The Original And The Rebuilds Have Distinct Endings
At this point, Evangelion can be considered a "choose your own adventure" series. All the endings have basically the same message - embrace life and yourself - but the delivery of said message varies wildly. Fittingly, 3.0 + 1.0 reuses imagery from The End of Evangelion, but with much different contexts.
Both films end with Shinji alone in a new world with a girl as his companion. In EOE, he and Asuka sat alone on a lifeless shore. In 3.0 + 1.0, however, Shinji runs off with Mari into our live-action world, and their relationship isn't burdened by the same dysfunction that had defined Shinji and Asuka's.