Is there a difference between "thinking of Jews as misers" and "thinking of misers as Jews?" No. But there's a big difference between thinking of a miser as a Jew, or thinking of a Jew as a miser, and thinking of misers as Jews, or thinking of Jews as misers.

I'd question whether it makes sense to talk about "a stereotypical" any ethnic group, because any group will have a range of stereotypes, which are not consistent with each other.