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No. Actually Babur was not Afghan.
Babur was a descendant of Tamurlane on his father's side and Genghis Khan on his mother's. He inherited Ferghana, a valley in Uzbekistan, where he is still revered.
The word Mughal is the Persian version of the word Mongol. He was actually Turco-Mongol, meaning he had Turkic and Mongol ancestry.
(Please note that many Central Asian states speak languages related to Turkish and so are related to the Turks. In fact, the Turks actually were supposed to have originated in Central Asia.)
Tamerlane was a Turk but claimed to be a Mongol, and a descendant of Genghis Khan, to be fearsome. They spoke language called Chagatai. Tamur's and Babur's biographies are written in that language.
Babur did conquer Kabul after being thrown out of his native Uzebkistan. He loved Kabul dearly and it became the only homeland he was left with after losing hope of recovering his original homeland.
The Lodhis are ethnic Pashtun and are not related to Babur.