In JMP®, when calculating principal components "On Correlations", the input variables are centered and scaled. Loadings are calculated by multiplying the eigenvectors by the square root of their eigenvalues.
When calculating principal components "On Covariances", the input variables are centered only. Loadings are calculated by multiplying the eigenvectors by the square root of their eigenvalues, and then dividing by the standard deviations of the input variables.
The loadings obtained by the "On Correlations" or "On Covariances" methods have the same interpretation. They represent correlations between the input variables and the principal component scores.
[Previously JMP Note 54434]