The Indian matchlock musket is called toradar.
Firearms were introduced into north India at large by the founder of the Mughal empire, Babur. He used them in great quantities during his invasion of the Indian subcontinent from Central Asia. One of his two master gunsmiths was nicknamed "The Ottoman", suggesting that is where the technology initially came from.1
Over time, Indian muskets further developed into their own characteristic styles, with more Persian influence. Mughal muskets are typically made of very good steel, enabling the use of higher charges of gunpowder. Their long barrels make for improved muzzle velocity, firing more accurately at longer ranges, provided the inside of the barrel is kept sufficiently clean as to minimize friction.
1. Kenneth Chase. Firearms: A Global History to 1700. Cambridge University Press. 2008
Robert Elgood: Firearms of the Islamic World in the Tareq Museum, Kuwait. I.B. Tauris Publishers. London / New York, 1995.
Lord Egerton of Tatton: Indian and Oriental Arms and Armour. Dover Publications; Revised edition, 2002.