Qemu is a user space system emulator. It can emulate in software different architectures like ARM, x86, etc. It can also emulate drivers, networking, disks, etc. Is called via the command line.
The reason you'll see Qemu/KVM a lot is because Qemu is the emulator, the things actually running the VM. And it utilizes KVM (on linux, OSX has HVF, for example) to accelerate the VM when the host architecture matches the VM's.
Libvirt is an XML based API on top of Qemu (and others). It allows you to define networks, VMs (it calls them domains), and much more with a unified XML schema through libvirtd.
Virsh is a CLI tool to manage libvirtd. Virt-manager is a GUI to do the same.
Proxmox is Debian under the hood with Qemu/KVM running VMs. It provides a robust web UI and easy clustering capabilities. Along with nice to haves like easy management of disks, ceph, etc. You can also manage Ceph through an API with Terraform.
Xen is an alternative hypervisor (like esxi). Instead of running on top of Linux, Xen has it's own microkernel. This means less flexibility (there's no Linux body running things), but also simpler to manage and less attack surface. I haven't played much with xen though, KVM is kind of the defacto, but IIRC AWS used to use a modified Xen before KVM came along and ate Xen's lunch.
If you actually played with Xen you'd know it's not actually easier to manage. And increased security claims are dubious at best, as same thing that would be attacked (dom0 managing the whole thing and running linux) have direct unfettered access to xen microkernel. There is reason many sites migrated away from Xen to KVM. Also many Xen drivers de facto run part Linux dom0 instance so you don't even get that isolation.
We ran Xen for few years, as KVM at first was still not as refined and Xen was first to mature market, and it was just million little annoying things.
KVM offers far simple and straightforward management. A VM is just a process. You can look at its CPU usage via normal tools. No magic. No driver problems.
AWS switched to KVM, and even a lot of AWS systems that report themselves as Xen are running as KVM with a compat shim to say it's Xen.
You're going to need dom0 (a "control domain") on any Xen host. Gotta have something running xl and the rest of the toolstack for managing it. dom0less technically exists but the drawbacks mean it's not really usable by most people in a production situation.