What's the difference between old Mongolian and new Mongolian?

By definition, the difference lies in writing letters:

Ancient Mongolian, used by Chinese Mongolians;

Traditional Mongolian (commonly known as old Mongolian) is improved from Uygur letters, followed by two variants: Totem Mongolian (тод? сэг), Arigari font (али-гали? сэг) 。

Neo-Mongolian, used in Mongolia:

The new Cyrillic alphabet adopted after Mongolia's independence (кирилл? сэг, commonly known as the new Mongolian language).