A seismometer is the internal part of the seismograph, which may be a pendulum or a mass mounted on a spring; however, it is often used synonymously with "seismograph".
Seismographs are instruments used to record the motion of the ground during an earthquake. They are installed in the ground throughout the world and operated as part of a seismographic network. The earliest "seismoscope" was invented by the Chinese philosopher Chang Heng in A.D. 132. This did not, however, record earthquakes; it only indicated that an earthquake was occurring. The first seismograph was developed in 1890.
A seismograph is securely mounted onto the surface of the earth so that when the earth shakes, the entire unit shakes with it EXCEPT for the mass on the spring, which has inertia and remains in the same place. As the seismograph shakes under the mass, the recording device on the mass records the relative motion between itself and the rest of the instrument, thus recording the ground motion. In reality, these mechanisms are no longer manual, but instead work by measuring electronic changes produced by the motion of the ground with respect to the mass.
A seismogram is the recording of the ground shaking at the specific location of the instrument. On a seismogram, the HORIZONTAL axis = time (measured in seconds) and the VERTICAL axis= ground displacement (usually measured in millimeters). When there is NO EARTHQUAKE reading, there is just a straight line except for small wiggles caused by local disturbance or "noise" and the time markers. Seismograms are digital now - there are no more paper recordings.