The origins of Mongolian people are said to have been a group of nomads from North-East Asia, however, people still have different claims and theories for ethnic Mongolian origins.
While Mongolians are not Turkic per se, Mongolians do share phenotype and cultural traits with Central Asian countries. The thing to note is that “Mongolians” are not one homogeneous group of people but rather a mix of different tribes and clans from Central – North-East Asian steppes.
While some Mongolians can look vastly different from each other (some having blond hair or green eyes with fair complexion vs Black hair/eyes and dark complexion) we Mongolians still consider ourselves as ethnic Mongolians (though fair looking people are in the minority). There are about 20 or so sub-ethnic Mongolian groups such as Buryats, Durvud, Oirats, Uzemchin, etc, so depending on someone’s ancestry, there is a range in look.
When the Mongolian Empire was founded in 1206, all the clans and tribes that Chinggis Khaan united were called Mongol. As the empire expanded, Mongols from medieval times settled in the conquered lands of Russia and Central Asia. They even adopted the local religion and assimilated it into the local culture, so you will find Mongolian-looking types of people in Western Asia, Central Asia, Russia, Korea, and China.