Yes, well, you're sort of right. But there are lots of changes in between, that are small changes when looking at the fate of the world, but big in terms of the characters themselves. For example:
Lavos Timeline: No forest in Zenan, Magus is worshiped in Medina Village, humans die of starvation in 2300 AD, etc.
Keystone Timeline 1: Forest is planted in Zenan, Medina Villagers worship no one, the humans live peaceful lives with FATE in the future.
See? There are differences. But, if you look in a universal point of view, your look is just as accurate.