There are many differences between the Richter scale and the Modified Mercalli scale. Some of the differences are that the Richter scale measures the magnitude of the earthquake, while the mercalli scale measures the intensity of the quake and the damage caused. And lastly how they are measured.
While the Richter scale measures the magnitude of the quake. To do this you have to have a seismograph to measure the shaking that goes on during the quake. It usually measures the activity underground. The magnitude of an earthquake can go to any height. And for every level of magnitude the scale increases by a force of thirty-one times that of a magnitude a full level below it. Unlike the Mercalli scale this way of telling how much shaking went on it has no upper limit to how much shaking can occur, even though the highest ever recorded was an 8.9 magnitude.
On the other side the Mercalli scale measures the amount of damage caused by the shaking. There are twelve levels that this can have ranging from barely noticeable to waking people up and even to knocking buildings down. While the Richter scale is a mathematical thing the Mercalli is only based on what it looks like not how much shaking actually occurs. This has a bad side that most of the levels are pretty much the same. The levels are blurred also not being very clear.
The only other difference is how they are measured. The Richter has a very precise way of measuring it. While the Mercalli is pretty much just how bad it looks not how bad it actually is.