To understand what the XAPI is and how it can be used please take a look at this demo I wrote: How to install ipython on XenServer and test XAPI. As we can see the XAPI is an elegant way on top of the hypervisor itself that exposes some more advance API operation to help to control and managed the VM and hypervisor live cycle.
In a very simplistic way you can think of Xen as a 'hypervisor kernel'. The kernel itself may be difficult to use so we need some management software bundled with it.
It is similar comparing Linux kernel and a distribution together. It is hard to use the kernel on its own, we need a more user friendly tools to do this and this is the place where GNU toolchain is coming into play.
Once we understand this it is now easy to understand this FAQ: What's the difference between Xen hypervisor (from xen.org) and Citrix XenServer or XCP?
If you understood what the last link is about please take a look at these for more advance comparisons:
Here is an example showing the differences between the XenServer and Xen management cli: