Before the game even begins, it's established that Tiberium is continuing to mutate and grow at an uncontrollable rate. Kane shows up to a GDI council meeting, proposing an alliance, as he has found a way to use the Tacitus to construct a way to stop the spread of Tiberium. Kane has the knowledge, but GDI has the funding and resources to make it happen. With no real options, the alliance is accepted, and GDI and Nod begin working together on the Tiberium Control Network, or TCN.
The game starts out as you being a commander for the GDI, in a further departure from the usual, you're given a name, and even a wife. You are Commander Parker. During the Incursion War Commander Parker suffered serious injuries in stopping the destruction of the GST (Global Stratospheric Transport) Methuselah, which caused him to lose his sight. He was given optical implants which were created using technology gained from the Tacitus, an alien artifact that was recovered by the Brotherhood of Nod in the events of 3. Kane, however, has a plan for the TCN, he plans on using it to activate the dormant Scrin tower - Threshold 19 - to finally reach "ascension". Commander Parker is the last surviving individual with the optical implants made with the Tacitus' technology, and these implants are linked to the TCN and Threshold 19.
You go through a couple missions as a GDI commander as an introductory campaign to the game, and are then presented with the choice of siding with either GDI or Nod.
The overall results of the end of the two campaigns remain the same, but there are small differences between the two.
If you play as the GDI, Colonel James, your superior, leads you on a campaign against Nod. James hates Kane and the Brotherhood, and she believes that Kane is attempting to bring back the Scrin, as she lost her family to the Scrin, which Kane called to Earth during the events of 3. In one mission, you are evacuating a city under siege by Nod Separatists, dissatisfied with the GDI/Nod alliance. During this mission, your wife is killed. James offers her sympathies, but tells Parker to focus his anger on Nod, as they were the ones responsible for her death. In this war against Nod, Col. James even goes so far as to defy a General and General Secretary who ordered her to stand down, and attempted a coup. She attempts to assassinate Kane at a large gathering of Nod followers, where Kane was on stage giving a grand speech. This, however, was a merely a body-double, and Kane remained at large. James and Parker confront Kane at Threshold 19, where they are successful in defeating the defending Nod forces, James and Parker enter Threshold 19. Kane appears before Commander Parker and addresses him, during this moment, Kane reveals that Col. James knew everything about the incident that killed his wife, and hadn't told him the full story. It turns out that your wife had actually died in an incident of friendly fire, and Col. James kept this information from him in order to keep him against Nod. Col. James then appears and opens fire on Kane, then shoots Parker, fearing that his implant will activate Threshold 19. Before she can deliver the killing blow, Kane reappears and strangles Col. James, before Parker's implant activates the portal inside Threshold 19. Kane thanks Parker, and steps through the portal, Parker then blacks out.
In the Nod Campaign, the initial stuff stays the same, but Kane has you go to numerous TCN Nodes around the world so that they can be aligned with Threshold 19 so that Kane may ascend. After a few missions, it becomes evident that as Parker is the last holder of the optical implants, the rest were killed by Gideon, the leader of the Nod Separatists, Kane needed to keep him safe. To this end, Parker was forced to undergo extensive surgery to effectively become Kane. Parker was to be Kane's eyes and ears, and act as the face of Kane in the public eye, while Kane himself operated in the shadows. Gideon's headquarters was finally discovered, and Parker led Nod forces to capture the false prophet at Kane's command. However, during a victory speech, Parker was shot by a sniper, and nearly died. After a hectic battle between Nod, Rogue GDI forces, and Parker's own forces using stolen GDI tech, he was saved. GDI took the Threshold, and it now it was time for Nod to take it back to begin the final preparations for ascension. After a hellish battle, Kane and Parker enter Threshold 19, and Col. James once again appears, but mistakes Parker for Kane, and fires. At point-blank, the wound was not instantly fatal, but Parker would not survive unless he got immediate medical attention, which wasn't going to arrive. Kane shows up and strangled Col. James just as Parker re-awoke, giving him enough time to open the portal of Threshold 19 open. Parker's wife rushes to his side as he's slowly dying, she cries to Kane that he assured her Parker would be fine. Kane response that he thought he would be, but that humans are fragile, and then steps through the portal.
The end result, no matter which side you chose, is that Kane and the rest of Nod ascended to an unknown location. With the successful activation of the TCN, Tiberium started to vanish across the world , as the TCN nodes were harvesting and processing it all on a massive scale.
However, there is still zero news on the whole "Scrin invasion" thing that was foreshadowed in 3, and considering how CnC4 was supposed to be the end of the Tiberium franchise, I doubt we'll ever know.