Managed hosting is used in at least two different ways:
* As a synonym for dedicated hosting. E.g. you rent a machine, and run what you want on it. And have to patch stuff etc.
* As a separate tier of service above dedicated hosting where the hosting provider is responsible for running the services on the machine. Some managed hosting providers will take responsibility for scaling too, though often it will be a semi-manual process.
Managed hosting in this second sense is to serverless what dedicated hosting is to "regular" cloud instances.
You might even toss in running managed services externally in the second definition, for example DNS for your own domain - pretty much every service small to large offers a DNS hosting service with your account, typically at no charge. Otherwise, you'd have to run your own server, etc.
* As a synonym for dedicated hosting. E.g. you rent a machine, and run what you want on it. And have to patch stuff etc.
* As a separate tier of service above dedicated hosting where the hosting provider is responsible for running the services on the machine. Some managed hosting providers will take responsibility for scaling too, though often it will be a semi-manual process.
Managed hosting in this second sense is to serverless what dedicated hosting is to "regular" cloud instances.