seismometer \Seis*mom"e*ter\, n. [Gr. ??? an earthquake + -meter.] (Physics) An instrument for measuring the direction, duration, and force of earthquakes and like concussions. seismograph \Seis"mo*graph\, n. [Gr. ??? an earthquake + -graph.] (Physics) An apparatus for registering the shocks and undulatory motions of earthquakes. seismogram \Seis"mo*gram\, n. [Gr. ? earthquake + -gram.] (Physics) The trace or record of an earth tremor, made by means of a seismograph.
basically, you just need to understand the differences between "meter" "gram" and "graph" an Xmeter is something that measures X at a given time, position, frequency, or whatever. an Xgraph is also something that measures X, but it does it for a number of times, frequencies, positions, or some other variable. an X gram is the output of an Xgraph. It is generally a graph with X on one axis and whatever it is a function of on the other.
so a seismometer is something that has a display of intensity of the earthquake at a given moment. a seismograph is something that records this intensity as a function of something else (in this case, time) and a seismogram is the recording made by a seismograph.