Sure and yes, your summary is fine, "reflect the funds that are safely stored offline".
The hot/cold wallet allows you to have a proxy representation of your local/cold wallet assets (masternode collateral) via the hot wallet (VPS).
In other words, you can shut down your local windows/Linux wallet as you please or leave it open for staking only (if the coin supports POS). Meanwhile, the hot wallet (vps) is on a highly secure and high reliability server infrastructure that you can shop around for. On top of assuring a high-reliability connection to the coin network, it can also reduce the attack vector to your direct wallet. If someone were to attack your hot wallet (vps) it would merely be the equivalent of cyber-vandalism with very little actual damage done. It could result in an interruption to MN rewards but that's better than a focused attack on your local machine if the scenario of the local machine is to be left on constantly.
Most masternode setups are hot/cold wallet setups. It would be easier to list coin projects that haven't started with hot/cold setup support and I can only think of one: Binarium. But I wrote a guide to setup a hot/cold setup for Binarium.