I am wondering about the equivalence of two notions of a "nilpotent orbit".

The first notion, which I am familiar with, is as follows: given a lie group $G$ and a lie algebra $\frak{g}$, the orbit of a nilpotent element $n \in \frak{g}$ under the adjoint action of $G$ on $\frak{g}$ is called a $\textit{nilpotent orbit}$.

I encountered a seemingly different notion in Example 4.2 of the following survey on variations of Hodge structures. http://people.math.umass.edu/~cattani/ICTP/cattani_vhs.pdf In this setting, a nilpotent orbit is a certain map from a product of copies of the upper half plane to a certain space of filtrations of a complex vector space.

These two notions don't seem to obviously coincide, but since they share the same name, I would hope that they are related.

Is this the case?