Q: Why does @RISK report both regression sensitivity and correlation sensitivity? Should they not give the same result in terms of relative ranking of input variables?
A: While regression and correlation are related ideas, they are fundamentally different.
Regression analysis implicitly assumes a linear cause and effect relationship between input variables and the output and then tests to see how good that assumption is. Regression fits the data to a line (for one input) or a surface (for multiple inputs). If the R-Squared value reported is high enough (the definition of "high enough" depends on the situation), the fit was good and the linear model is a good reflection of the relationship between the inputs and output. If the R-Squared value is too low, the regression model is not an accurate reflection of the relationship between the inputs and outputs. See Also Definition of Standard "B" Coefficients.
Correlation assumes no cause and effect relationship between inputs and outputs. In simplified terms, it simply asks the question "when this input is big, does my output tend to be bigger (a positive correlation) smaller (a negative correlation) or does the value of the input have no effect on the output (zero correlation).