
In the server virtualization area the main type 1 (or bare-metal) hypervisors are: VMware ESXi, Microsoft Hyper-V, Xen and KVM. For the public cloud IaaS solutions the most used are Xen (AWS use a custom version) and Hyper-V (in Azure). For the on-prem infrastructure, ESXi is the most used, followed by Hyper-V and KVM.
Both Xen and KVM are just a family, because each Linux distribution have it’s own version those hypervisors. If we speak about XenServer we are looking at the Citrix version of Xen (Citrix has bought the commercial version of Xen several years ago), or if we speak about RHEV we are considerin the RedHat implementation of KVM (RedHat was one the first to push on KVM as a possible shift from Xen).