The System p servers, formerly known as the p Series or RS/6000 systems, are based on IBM's Power chip and typically run IBM's AIX version of Unix. A common use of the System p is as a large database server.
System i servers are the former AS/400 mid-range servers, also based on Power chips but running the i5/OS operating system often used by small and mid-sized business.
Both server lines also run Linux; PowerVM may be used with any of the three operating systems.
PowerVM is IBM's established server hypervisor and related software that subdivides physical servers into LPARS or logical partition units, each with its own virtualized operating system and application. PowerVM was formerly known as Advanced Power Virtualization.