A PKI is the whole system described in the preceding sections - one or more CAs, their procedures (defined in their CPS's) for vetting applicants for certificates, and for handling and issuing certificates, and the SSL software used by entities to send, receive, and check certificates.
The Internet has, in effect, its own world-wide PKI, based around internationally known CAs such as Thawte, VeriSign and others. An organization, such as a company, can set up its own PKI for use within its intranet or network.
The same SSL software and world-wide standards (such as certificate formats) would normally be used in either case. The principal distinction between the world-wide PKI and a private one is that in a private one the organization would set up its own CAs, recognized within the organization.