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I think you inversed the relationship. Multiple R is the correlation between actual and predicted values of the dependant variable. R2 is the modelâs accuracy in explaining the dependant variable. I think there is a testable difference.
Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is applicability: multiple $R$ implies multiple regressors, whereas $R^2$ doesn't necessarily. Another simple difference is interpretation.