Depends on company (and price).
Some just secure your server and you do the rest.
Some secure your server and install the software you need and you do the rest.
Some secure your server and install the software you need and manage all server related issues. You only deal with customers.
First and second is pretty common (and usually easy to find), the third is pretty rare and a bit more expensive.
It depends on the provider. There is no single definition for "managed" services. You'll want to make sure you have a clear understanding of what the provider considers to be "managed" before you sign up.
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We do quite a bit like setup the server, monitor your server, handle backup & recovery, security scans and Patching for our managed servers so at first glance it looks more expensive. It's not realy when you realise what you get for your cash... So you have to take each suppliers definition into consideration when pricing up a server.