There are two major types of phone system available for your phone system needs:  Key systems and Private Branch Exchange (PBX) systems.

A Private Branch exchange (also called PBX or Private Business exchange) is a telephone exchange that is owned by a private business, as opposed to one owned by a common carrier or by a telephone company. A PBX phone system is typically suited for businesses which require over forty extensions and it's primary function is to control the flow of phone traffic within an organization (similar to a switchboard).  Additionally, telephone sets, fax machines, modems and many other communication devices can be connected to a PBX as well

A key system or key telephone system is a multiline telephone system typically used in small office environments.  Key systems are noted for their expandability and having individual line selection buttons for each connected phone line, however some features of a private branch exchange such as dialable intercoms may also commonly be present.

source: wikipedia.org