Where is the divide between a computational scientist and a computational X (X = some natural science or discipline)? What questions could someone ask themself to decide which is the best route for them?
Your question implies that there is a firm line between them, but this is far from the case. I will be answering from my own position, where I see myself as a computational scientist, but I work in computational plasmas. Hopefully the difference I draw between them will be insightful.
As a computational scientist, I enjoy the mathematics and methodology behind solving the many equations that appear in my field (Poisson's eq, compressible N-S, Boltzmann eq, etc.). My advisor, on the other hand, couldn't really care less how the equations are solved, only that the solutions are found quickly and are "correct".
From this, the main difference I see between the two groups is whether the application or the methodology is the focus. I personally see the methodology as my focus, since after graduating with my PhD, I likely won't stay in plasmas. It is really more of a spectrum, with CS/Mathematics on one end, next to computational science, followed by computational X, and then the pure X, whatever that may be.
There is only an artificial difference. Computational X solves problems in X, i. e. physics. Most often, you specialize later in Computational science, so you get an X, lately. Computational science without the X doesn't make much sense, so you would have to study computer science or mathematics, to get the pure math or the pure informatics.
I've given an answer to this question here: Does Computational Science involve programming? I still think it to be true :-)