Let $R$ be a Noetherian normal domain with divisor class group $Cl(R)$ and Picard group $Pic(R)$ and we can consider $Pic(R)$ as a subgroup of $Cl(R)$. Consider the following two statements:
(1) There is a positive integer $D>0$ such that $D.Cl(R_{\mathfrak m})=0$ for every maximal ideal $\mathfrak m$ of $R$ .
(2) There is a positive integer $D>0$ such that $D$ annihilates $Cl(R)/Pic(R)$ .
Now my question is: Are these above two conditions equivalent ?