1) Virtual Servers:
They are commonly called VPS (Virtual Private Server) and are nothing more than virtual machines running through a hypervisor such as VMware ESX, Xen (free) or Microsoft Hyper-V. In these cases, a real server simultaneously executes a certain number of virtual machines on the same real hardware.
2) Cloud Server:
It is a version of the previous ones, but with very important advantages. In this case, it is also a virtual machine but executed on a cluster of servers mounted on Cloud. This means that the workload is shared between multiple machines that manage their resources centrally and generally with high-performance associated storage systems.
3) Dedicated Servers:
Here we already talk about real machines assigned to us exclusively, so it would be the "pure" dedicated solution. Its main advantage is that we can do exactly the same as with any server that we had in our table: install any operating system and have 100% of the hardware for ourselves. It's also very affordable.
4) Managed Servers:
This is a variety of the above, and not all providers offer them. It is a dedicated server to which we will not have full access to the command line. In return, the technical team of the supplier will be in charge of updating, fixing and maintaining the machine in perfect operation. In this way, we will be able to ignore management/maintenance to a certain extent, but enjoying complete resources and the possibility of requesting the installation of specific components and making adjustments tailored to our needs.