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My apologies for the title being vague due to length constraints.

What I'm asking is would the following two scenarios render a different result?

a) Having USD as the base currency and dividing the results of two currencies A and B to see the exchange rate of A to B

b) Having either A or B as the base currency and requesting

I think they would be different, but just want to make sure.

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Yes it would be different from retail individual point of view. The rates are different and the hops would give different results.

However if you are interested in rates if A to B, then in second scenario you directly get the rate for A to B.

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