As nouns the difference between seismograph and seismometer
is that seismograph is an instrument that automatically detects and records the intensity, direction and duration of earthquakes and similar events while seismometer is (geology) a device used by seismologists to detect and measure seismic waves and therefore locate earthquakes etc; a seismograph.
A seismometer is a device that is sensitive to vibrations. It works on the principle of a pendulum: a heavy, inert mass with a certain resistance to movement (i.e. inertia) due to its weight is suspended from a frame by a spring that allows movement. The energy from any seismic activity excites this “proof mass” as it is called by geophysicists, making it vibrate.