An earthquake magnitude is an objective measure of the energy released. It is based on seismograph readings, and is a single number that characterizes the size of the earthquake. The first methods for determining magnitudes were derived by seismologist Charles Richter, so although different algorithms are now used, these are still often called Richter magnitudes.
Intensities are another way of indicating the nature of seismic ground motion in a particular area, and the response of people and structures to that ground motion. It is somewhat subjective; intensities vary from being highest near the epicenter, to decreasing values at greater distances. The Modified Mercalli Intensity Scale is the one in common usage today.
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Notice the intensities for the Lancaster quske as shown above are all Roman numerals II and III - compare these to the description above for the Modified Mercalli Scale.