I've been wondering about what a "group algebraic stack" should be, and ran into the notion of a Picard stack.

I'm slightly confused by the terminology here.

Given an algebraic stack $\mathcal X$ over $S$, one can define the Picard stack $\mathcal{Pic}_{\mathcal X/S}$. Is this a Picard stack as defined in "Smooth Toric Deligne-Mumford stacks" by Fantechi, Mann and Nironi?

Are Picard stacks group objects in the category (or 2-category?) of algebraic stacks?