A VPS gives you dedicated server resources, but "managed" versus "unmanaged" describes a completely different question: who's responsible for keeping the server itself running correctly.
You get root access and full control — and full responsibility for OS updates, security patches, software installation, and troubleshooting anything that breaks. This is the right choice if you have genuine server administration experience or a technical team, and want the lowest possible price with full control.
The hosting provider handles OS-level maintenance, security patching, backups, and often 24/7 support for server-level issues — you're still responsible for your actual application/website, but the underlying server infrastructure is someone else's problem. For a business without dedicated technical staff, this is usually worth the price premium, since a poorly maintained unmanaged server is a genuine security and uptime risk, not just an inconvenience.
If "server administration" isn't something anyone on your team already knows how to do, managed hosting's premium is cheap insurance against downtime and security incidents you're not equipped to prevent or fix quickly. If you do have that expertise in-house, unmanaged hosting at a lower price point is a reasonable trade.