All over the place in Rosetta Documentation, I find the terms "repack", "prepack". But I have not found their definitions. I suspect that "repack" and "prepack" refer to conformational samplings where only amino acid side chains are moved, while the backbone remains fixed, but I can't be sure. Is it in this sense that these terms are used here?
What are the definitions of "repack" and "prepack" (in the common usage of these terms in the ROSETTA community)?
You're basically correct in your assumptions.
To solve the sidechain positioning problem, Rosetta uses "the Packer". This is a non-deterministic Metropolis Monte Carlo simulated annealing protocol, which attempts to find the lowest energy conformation of sidechains on a fixed backbone, assuming the sidechains come from a fixed set of rotamers.
The reason it's called the "packer" is that it was originally developed to find the optimal packing of sidechains in the hydrophobic core of proteins. It turns out that the packer is generally useful for combinitorial optimization of sidechain positioning, and can be used for design as well as packing. (Instead of choosing between rotamers of a single amino acid, you just add in rotamers of other amino acids too - the algorithm is residue-based, so the different number/kinds of atoms in different amino acids doesn't matter.) So sometimes you'll hear talk of "packing" even when the identity of the amino acid is allowed to change.
So what is a "repack"? Well, it's just a packing run where there's already a sidechain information. This is actually the most common use case, so in practice there's little difference between "pack" and "repack". The "re-" is used mostly to emphasize a change of sidechain conformation. Most notably, if the packer is applied after some other step. "Prepack" is simply the inverse - you pack the protein prior to some other step.
So in a typical protein-protein docking run you might prepack the starting structures to remove crystallographic artifacts or other issues with the input structure, then run docking, and then repack the proteins after docking to optimize the sidechains in the bound complex. On a technical level, there's no difference between prepacking, repacking, or even any "plain" packing that might happen during the docking stage. The only difference is a semantic one about where it fits conceptually in the protocol.