Xen is a hypervisor. XenServer is the product name from Citrix which uses Xen underneath. Xen Cloud Platform is actually the name of opensource xenserver.

You wouldn't use just Xen as a hypervisor, in most cases. Amazon uses Xen plus their own stuff on top.

To make it more complicated, there's also XenClient, which also builds on Xen. It's also mostly open source.