I'm not sure that they reduce to the same thing. In e.g. Newcomb's problem, if you reduce your two options to "P(full box A) U(full Box A)" versus "P(full box A) U(full box A) + U(full box B)", where U(x) is the utility of x, then you end up two-boxing, that's causal decision theory.

It's only when you consider the utility of different decision theories, that you end up one boxing, because then you're effectively considering U(any decision theory in which I one-box) vs U(any decision theory in which I two-box) and you see that the expected utility of one-boxing decision theories is greater.

In Pascal's mugging... again I don't have the math to do this (or it would have been a discussion post, not an open-thread comment), but my intuition tells me that a decision theory that submits to it is effectively a decision theory that allows its agent to be overwritten by the simplest liar there is, and therefore of total negative utility. The mugger can add up-arrows until he has concentrated enough disutility in his threat to ask the AI to submit to his every whim and conquer the world on the mugger's behalf, etc...