Fatalism seems to be the concept that any path taken will always lead to a given destiny. I think I identify more with causal determinism, wherein there is only one path.

Personally, I don't see much of a difference between those two, but I can see where one may view the former as more open-ended. If it's something divine pulling the strings or natural phenomena driving you to some fixed circumstances, I don't see much in the way of paths with either.

Regarding your last point, if you were given the exact identical states of everything down to the atom, why expect a different result? Because even if it's all the exact same, you set it in motion again, and again, and again, something on some level is going to vary each time. I don't know of any process or phenomena in the universe that, despite following many of the same basic processes as one another, results in the exact same results each and every time. There's always some variation, some divergence, something that despite everything clicks ever so slightly a different way, and that's basically why anything even is at all.

If you spun back the clock on this solar system, or even this galaxy, to the exact same conditions that gave rise to it and let it run again, I wouldn't bet on it coming out the same way, because each and every input is contingent on the other and any slight detail of those varies? Adds up and produces different results. The laws of nature are not nature, they're a good, educated attempt at understanding its operations, its processes, and they're undeniably useful, but it's wisest to remember just what they are, and what they are not. "The map is not the territory," as ol' Alfred Korzybski said.