What's the difference between Inner Mongolia and Mongolia?

It didn't make any difference. Inner Mongolia is divided in the order of naturalization by the central government. Inner Mongolia was originally planned by the Manchu central government, so it was called Inner Mongolia. After Outer Mongolia was controlled by the Soviet Union (so-called independence), the Soviet Union forced the implementation of the new Mongolian language (written in Russian letters). Today's outer Mongolians can hardly understand themselves. My brother has a classmate from outer Mongolia who asked him to recognize him in Mongolian on RMB. He said, it seems that he should understand Mongolian characters.