The definition of a managed server differs from hosting provider to hosting provider. The least you could expect is a dedicated server plus connectivity and a Windows, Linux or BSD Operating System on top of it, although you might expect a bit more. Offering back-up & restore functionality might be the first additional service that pops up in mind when talking about managed server hosting. Other services provided could be incident management, monitoring, or patching the Operating Systems, to name a few.
Although there are hosting providers with managed server offerings that will perform management of the customer’s applications (such as ERP systems, or specific software within certain verticals), many of them are drawing a line at the point where this client specific need fulfillment begins. So the management of client specific applications on top of the OS should not be considered as the norm for ‘managed server hosting’.