The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology based on measurements made of shallow earthquakes in California. Technically, the way it was developed means that it's the most accurate in California, and when using a specific type of seismograph; it's also not terribly accurate for very large earthquakes or distant ones. Scientists have since expanded on the methods Richter used, which now incorporate even more data that can be recorded about an earthquake. The USGS website about "Earthquake Magnitude Policy" says it this way:
"There is some confusion, however, about earthquake magnitude, primarily in the media, because seismologists often no longer follow Richter's original methodology. Richter's original methodology is no longer used because it does not give reliable results when applied to M> 7 earthquakes and it was not designed to use data from earthquakes recorded at epicentral distances greater than about 600 km. It is, therefore, useful to separate the method and the scale in releasing estimates of magnitude to the public."
"Moment is a physical quantity proportional to the slip on the fault times the area of the fault surface that slips; it is related to the total energy released in the EQ. The moment can be estimated from seismograms (and also from geodetic measurements). The moment is then converted into a number similar to other earthquake magnitudes by a standard formula. The result is called the moment magnitude. The moment magnitude provides an estimate of earthquake size that is valid over the complete range of magnitudes, a characteristic that was lacking in other magnitude scales."