After Mongols lost control of China (end of Yuan dynasty), there were many struggles between Mongols and Chinese as well as different Mongol tribes. These struggles weakened the integration among Mongols. After a successful but short-lived unification attempt by Dayan Khan, a more organized disintegration took place giving birth to Khalkha Mongols (formerly Jalair, Jaruud, Baarin etc), a more united Oirat (Western Mongols) and more distinctive Eastern Mongol tribes (Khorchin, Kharchin, Chakhar etc). Oirats had their own dynasties: Dzungar and Khoshuut khanates employed with politics with Tibetans, Kazakhs, Moghulistan and other Inner Asian entities. Khalkh khans gained more independence from the concept of unified Mongols. Eastern Mongol tribes were mostly employed with politics with neighboring Jurchens and Chinese.
When Manchu (former Jurchen) invaded Mongolia and China, Eastern Mongols were incorporated into their dynasty first, later China, Khalkha Mongols and then Western Mongols. Since, Eastern Mongols were invaded some time before others, different administrative division was applied based on the cooperation of tribes with Manchus and Mongol tribal units.
From this time, the political separation between Inner Mongolia and Outer Mongolia was more clear. Roughly speaking, Inner Mongolia included Eastern Mongolian tribes, while Outer Mongolia included Khalkha Mongol khanates as well as Oirat territories. Other Mongol entities also existed in Hulunbuir, Huh Nuur and Alasha.
In the last years of Qing dynasty and afterwards, many forms of independence movements took place like Bogd Khanate Mongolia, Japanese-sponsored Greater Mongolia based in Chita, again Japanese-sponsored Independent Inner Mongolia in Kalgan, infamous Manchu-Mongol Independence Movement etc: among those most popular being Bogd Khanate Mongolia. Bogd Khanate Mongolia was established by Khalkh nobles and Bogd Jebtsundamba in Huree, right in the center of Khalkh territories (current-day Ulaanbaatar). Many commoners and nobles in Inner Mongolia as well as Hulunbuir and some Huh Nuur Mongols agreed to cooperate with Bogd Khanate Mongolia. Khalkh conquests freeing Inner Mongolia from Republic of China was mostly successful until Russia and China called Bogd Khanate leaders for trilateral summit in Khyagta disabling Bogd Khanate Mongolia to expand their territory. Another thing happened was that Bogd Khanate Mongols freed Hobd territory from Manchu rulers incorporating non-Khalkh territory into their land.
In 1921, Mongolian People’s Republic was established mostly on the basis of Bogd Khanate Mongolia thus incorporating Khalkh territories plus Hobd, Dariganga and Khuvsgul. On the other hand, Inner Mongolia saw rather different developments: since in the last years of Qing dynasty, policies of the weakening government made eastern Inner Mongolia and Manchuria made targets for large Chinese immigration, Republic of China decided to divide Inner Mongolia into Chinese provinces. This resulted in independence movements and Mongol support for Mengjiang puppet state. During Chinese Civil War, Inner Mongolian communist activists gained autonomy of Inner Mongolia which was more attractive than being separately colonized provinces in a foreign country.
Conclusion: Separation of Mongol tribes into political entities started after feudalist period after Yuan dynasty. Geographic differences, interactions and political turmoils forced Mongols to have different political paths.