Describe morphisms of quotient stacks.

Question

Let $G,H$ be group schemes, acting on schemes $X,Y$ via $G\times X\to X$ and $H\times Y\to Y$. I want a description of a morphism $[X/G]\to [Y/H]$.

When $X$ is a point, we have $[X/G]=\mathrm BG$, the classifying stack. A morphism $\mathrm BG\to[Y/H]$ is equivalent to the following data:

1. a point $y$ of $Y$;
2. a homomorphism $G\to H_y$, where $H_y\subseteq H$ is the stabilizer of $y\in Y$.

I want to know if there is a similar description for a morphism $[X/G]\to[Y/H]$, i.e. some geometric information (such as a point) together with a group homomorphism (or some equivariant morphism).