Mughal is nothing but a Persian rendering of the word “Mongol”. Genghis Khan and his immediate descendants who invaded Persia and India in the 13th century were known as “Mughal Kafirs” in Persian literature. Mughals invaded Afghanistan just like they later invaded India.
Tolui Khan, the son of Genghis Khan, who in 1221 invaded Persia & utterly defeated, devastated, and massacred Khorasan was called a “Mughal” in Persian Chronicles. The word for 'Mongol' in Persian is 'Mughal' - from Sharjat Ul Atrak.
Likewise, the Mongol armies of Genghis Khan's grandson Mongke Khan who invaded India in 1245 were known in Persian literature as “Mughal infidels”. Yes, the Mughals of Babur's line were speakers of the Chagatai language which is a Turkic language. As such, they were not direct patrilineal descendants of Royal Mongol lineage even if they claimed matrilineal descent from Genghis Khan.
Yet, the ultimate origin of these Altaic languages and their speakers is the Altai mountain range in Western Mongolia. Besides, there were clear ethnic differences between “Turks” and “Mughals” (even if “Mughals” themselves spoke a variety of Turkic language).
Even as late as the 16th century, when there was a lot of “admixture” between “Turks”, “Tajiks” and “Mughals”, there were still some differences in Phenotype. For the Author of Tarikh I Rashidi, A “Mughal” typically had Mongoloid features like a short nose and no facial hair. We certainly come across such “Mongoloid features” of early Mughals of Babur's line in their paintings.
Neither Uzbekistan nor Afghanistan is the original homeland of Turks and Mughals. Before these Turkic and Mongol invasions from the East, the region today known as Uzbekistan was inhabited by an Iranic people known as Sogdians who were of Europoid Phenotype with light eyes.
Even Babur claimed himself to be a descendant of Chagatai Khan son of Ghengis Khan. Khan's title was not a Muslim title but a Mongol title of respect.