Davidson arrives on an alternate Earth where the Abraham Lincoln statue is now an "Ape Lincoln" statue with a plaque that says it is in memory of General Thade. Davidson is then surrounded by police officers and firefighters who are apes. According to Helena Bonham Carter, "Thade beat him there." General Thade, although imprisoned after the battle, apparently escaped some time later and left Ashlar in some kind of spacecraft. Davidson was sent back to the Earth of 3,000 years earlier, but Thade, although leaving much later, ended up earlier than Davidson. The reason this happened is that the order in which someone exits the electromagnetic storm is the reverse order of whoever entered it. In other words, it's an inverse relationship. This is the reason the Oberon crashed on Ashlar before Davidson did and Pericles landed after Davidson.
One theory is that Thade arrived on Earth somewhere in the 19th century. There, he staged a revolt among the apes, not unlike Semos once had done, making the apes once again the dominant species on the planet. So when Davidson arrived 200 years later, he found his own planet conquered by the apes, and a monument erected in Thade's honor. Another theory is that Thade arrived after the Oberon went through the electromagnetic storm in 2029 and that Davidson actually returned on 10/26/2155, the last year seen on the chronometer. Rather than an alternate timeline, Thade would have led the apes of Earth without changing the past centuries and had the Lincoln monument changed in his honor during the 100 or so years before Davidson's return. This explanation would explain why Washington still looks the same as it ever did. It has been suggested by some that Davidson may have landed on a future version of Ashlar that appears similar to Earth. However, the planet that he lands on at the end of the film does not appear to have two moons, and given that Davidson set a course for Earth's location at the end, it would be unlikely that he'd end up on another planet. It has also been suggested that Davidson landed on a different planet, neither Ashlar nor Earth, that is ruled by apes. If this is so, then the reason that their Washington D.C. looks similar to ours is unknown. Another very unlikely theory is that the anomaly took Leo Davidson to an alternate universe where Earth is ruled by apes, and the Thade in that universe is not the Thade from Ashlar, but a version of him that lived on an alternate Earth.
According to Tim Burton, this ending was a nod to a similar ending in the original novel, but also meant as a prelude to a sequel that was never made. Rich Handley's Timeline of the Planet of the Apes contains the following note: "Ty Templeton, author of Revolution on the Planet of the Apes, had intended, in his initial concept for that title, to explore how Thade changed Earth's history. Fox, however, opted to keep the two Apes incarnations separate. Ian Edington and Ben Abnett had also planned to reveal Thade's fate in an unpublished storyline for Dark Horse, which would have featured characters from Semos' world visiting Earth's past in the Oberon's remaining pods, via the anomaly. Their plan had been that the Earth Davidson returned to was not the same Earth he left, but rather a parallel planet similar to that which Ulysse Merou returned to in Pierre Boulle's novel, The Monkey Planet. The Thade name, Edington says, would have been a powerful ape dynasty on that Earth, much like the Kennedys or Rothchilds."