Non clown hosting
Colocation (as mentioned yesterday) gives you some space, some power, bandwidth, a network allocation of some kind (and/or ability to route your own stuff), and hopefully some decent HVAC to keep everything cool. It's your hardware in their space, and if something breaks on that stuff, you get to fix it. What if a drive fails? That's on you. Your switch or router goes insane? Same deal: that's all you.
You might be able to get some "remote hands" service from the provider for very simple tasks: reboot something, take a picture of the (blue) screen, that kind of thing. Some also let you pay them to go and do other stuff with a higher degree of complexity. Read the fine print.
Managed hosting is where you get access to a box somewhere, and are usually given root on it. You can do about what you want to it, but beware of the "spheres of support" as we used to call it - the hosting company's support people will only go so far. You might want Debian, but they only do RHEL. You get the idea. You can probably ask them to do kernel upgrades, troubleshoot why it's being slow or seems to be down, install and configure certain things for you, and so on.
This is a good outline what kind of hosting options are availabel out there beyond the cloud. Our hosting of choice is Hetzner.