Games and their Servers

To make this less abstract, let's look at how some actual popular games split between local and virtual private server setups:

• Minecraft is honestly the perfect example for us, because it supports both options. You can host a world straight from your own PC for a quick session with friends, or you can point everyone toward a virtual private server that someone else owns and that stays online permanently. That flexibility is exactly why it's such a common first choice for people learning to run their own server — you can start local, then graduate to dedicated hosting once you want something more permanent.
• League of Legends goes the opposite direction — there's no local hosting option at all. Every player connects to Riot Games' dedicated servers to experience the shared map and match state together. You can't just spin up a copy on your own PC; the entire game is built around that always-on, centrally hosted world.
• Counter-Strike (both the older CS:GO and current CS2) also supports both setups. You can quickly throw together a local server to mess around with friends, or hop onto a virtual private server for the real competitive experience with strangers or organized matches.

The takeaway: not every game gives you the choice. Some are built to only work one way. So before you go all-in trying to set up a server for a specific game, it's worth checking what that game actually supports — no point building a virtual private serverer for a title that only runs local sessions, or trying to host locally for a game that requires a dedicated setup.