Is Vagrant an operating system by itself? If Vagrant (and similar software) uses to orchestrate, install and continuously upgrade one or more OSs on a single machine, isn't it some kind of an operating system by itself?

Or it actually virtualizes an OS on top of an existing OS and doesn't operate as an OS by itself?
No, Vagrant is a tool for creating virtual environments, which it then can run inside a virtual machine (originally only using Virtualbox, but nowadays also KVM and VMware among others).

The environment created by Vagrant is, however, a fully virtualized OS (e.g. Ubuntu).