Xen virtualization

Hello, noticed following today:

Chapter 19 - Virtualization
Section: External and in-Kernel Hypervisors
External to the host operating system kernel: Xen

Section: Dedicated Hypervisor
Xen and VMware ESX (and related friends) is an example of a hypervisor embedded into an operating system.​

How can the Xen be embedded into OS while also being external?
Per wiki, Xen should be Type-1 (native/bare-metal) running on host's hardware.

Could you please clarify which statement is correct?
Or is it meant it's external to the OS kernel while still being embedded/part of into OS?

Thank you