I used the same seed as a random LPer, walked to the same spot as him in the video but world generation differences start to appear

What I expected to happen was that my game would generate the exact same world as the LPer

What actually happened was that minor to average differences were generated. Blocks, grass, trees, reeds etc. Especially jungles are very different.

Steps to Reproduce:
1. Use a seed
2. Walk a few hundred blocks away from spawn
3. Use the same seed again or on another computer or something

I don't know if this happens for everyone, but it always happens with me. It was the case when 1.3 was new, and it still happens here. I got a picture, the upper picture is the world the LPer has, the lower is the world I have. The apples show that we are both in 1.4 and both he and I did not plant/chop down any trees/reeds in that particular area.

Extra detail:
It appears to happen when new chunks get generated, not when the world has just been loaded.