boston
Davidson crash landed on a foreign planet some time in the future. The mother ship went looking for him and crashed on the same planet. But the mother ship crashed at some earlier time and changed the future of this planet. The monkeys on board the mother ship evolved to what Davidson now sees on the plant. This part is explained in the movie.
Now take that same thought to when Davidson leaves the planet. He takes the pod and travels back in time to earth and crashes at the Lincoln Memorial and Lincoln turns out to be Thade. Davidson left Thade alive back on the foreign planet in the mother ship. So, Thade had to have escaped, fixed Davidson's submerged pod from the lake and followed Davidson back to earth. But, Thade time warped further back in time, to Lincoln's time and changed the course of history. That's why you see Thade as Lincoln. Thade changed history and in turn became president Lincoln and changing the future. The future earth that Davidson now crashed landed
Now take that same thought to when Davidson leaves the planet. He takes the pod and travels back in time to earth and crashes at the Lincoln Memorial and Lincoln turns out to be Thade. Davidson left Thade alive back on the foreign planet in the mother ship. So, Thade had to have escaped, fixed Davidson's submerged pod from the lake and followed Davidson back to earth. But, Thade time warped further back in time, to Lincoln's time and changed the course of history. That's why you see Thade as Lincoln. Thade changed history and in turn became president Lincoln and changing the future. The future earth that Davidson now crashed landed