The underlying architecture that allows you to create a VPS are of different types, but the two most popular ones are:
- OpenVZ
- Xen

They both allow virtualization, with Xen being different in that it does not allow you to oversell. Any resources allocated to a Xen VPS are dedicated to it in every way and form. Those resources cannot be 'reused' or 'oversold' to any other container. This is also why Xen VPS's are usually expensive compared to OpenVZ.

Now some of the most popular softwares that help you MANAGE these VPS's, that I know of, are:
- SolusVM
- Virtpanel
- Virtuozzo
- HyperVM