Public transport (also public transportation, public transit, or mass transit) comprises passenger transportation services which are available for use by the general public, as opposed to modes for private use such as automobiles or vehicles for hire.

http://en.wikipedia.org/wiki/Public_transport

A rapid transit, metro, subway, underground, or elevated railway system is an electric passenger railway in an urban area with high capacity and frequency, and which is grade separated from other traffic.^[1][2] Rapid transit systems are typically either in underground tunnels or elevated above street level. Outside urban centres rapid transit lines sometimes run grade separated at ground level.

http://en.wikipedia.org/wiki/Rapid_transit