Actually, no, a galactic algorithm and nongalactic may give different answers.

Consider the TSP problem from TFA, in this case two approximation algorithms were presented, one marginally better, meaning the answer would be different.

I believe channel capacity encoding was like this as well, but that is not in my wheelhouse.

I was trying to keep things simple, by talking about algorithms that have precise answers (such as multiplying 2 numbers or sorting a list). In that case you would expect the galactic and nongalactic algorithms to give the same answer, but with different time and space characteristics. Perhaps I should have been clearer.