A seismometer and seismograph are somewhat synonymous in they are both instruments for the recording of movements of the earth associated with earthquakes or other seismic sources such as explosions. Seismographs combined the detection and recording in one instrument. Seismometers may be connected to multiple detectors called geophones. This is how these instruments are used in the petroleum industry to image structures in the subsurface for oil exploration.
Seismogram is the graphical output from these instruments. See example:
By using multiple seismograms from around the world seismologists can pinpoint the location of earthquakes or volcanic activity anywhere on the planet.