Xen is a microkernel, loosely based on the Nemesis OS from the University of Cambridge. Instead of running traditional POSIX software, this microkernel runs software in ring 1 using a very special system call API. DomU and Dom0 support for Linux means that Linux has been ported to run on top of this special system call API.
But this doesn't mean Xen is now in Linux. Xen is still a separate OS with it's own memory manager, scheduler, device drivers, etc.
OTOH, KVM is a device driver for Linux that let's you run virtual machines under Linux. You're still using the Linux scheduler, memory manager, device drivers, etc. KVM is fundamentally a part of Linux.
For another point of reference (with less confusing terminology), L4 is pretty much the same thing as Xen and L4Linux is equivalent to Linux dom0/domU support.