Short answers, pulled from the story.
In 515 BCE, the Persian King Darius I annexed the Indus Valley and transformed the ancient Sanskrit word Sindhu into the Persian Hindu. This linguistic shift began with a Proto-Iranian sound change between 850 and 600 BCE where the sibilant s became an h. The term originally denoted the fifteenth domain created by Ahura Mazda before expanding to cover the entire subcontinent.
During the Delhi Sultanate which ruled from 1206 to 1526 the term Hindustan acquired a precise political geography referring specifically to the territories of northern India, the Punjab, and the lands of the Indus. The ruling elite made a deliberate distinction between Hindustan and Hind where the former referred to the Gangetic plains and the Doab region under Muslim political control. Babur described Hindustan in his memoirs the Baburnama as bounded by the ocean on the east, south, and west yet the term often excluded Bengal and Bihar.
In the 18th century the last Gorkhali King Prithvi Narayan Shah of Nepal self-proclaimed his unified Kingdom of Nepal as Asal Hindustan or Real Hindustan to assert Hindu sovereignty over a subcontinent increasingly ruled by Islamic Mughal emperors. Shah's proclamation was designed to enforce the Hindu social code of Dharmashastra over his reign and to designate his country as the only land truly inhabitable for Hindus. He referred to northern India as Mughlan the country of Mughals and labeled the region as infiltrated by Muslim foreigners to create a stark dichotomy between his Hindu kingdom and the Muslim-ruled north.
In 1792 the British geographer James Rennel published an atlas titled the Memoir of a Map of Hindoostan or the Mogul Empire which depicted the entire Indian subcontinent. Rennel's map conflated the terms Hindustan, India, and the Mughal Empire in a way that reflected the confusion and overlap of these concepts during the colonial era. British officials and writers often believed that Indians used Hindustan to refer only to North India excluding the southern regions.
The 1940 Lahore Resolution of the All-India Muslim League demanded sovereignty for the Muslim-majority areas in the northwest and northeast of British India which came to be called Pakistan in popular parlance. The Dominion of India was referred to as Hindustan a naming convention that sparked intense debate among Indian leaders. British officials adopted these two terms using Hindustan to describe the Hindu-majority Dominion of India a usage that was rejected by Indian leaders who insisted that the new nation should be called India not Hindustan.
The Hindustani language the lingua franca of the northern Indian subcontinent derives its name from the shortened form Hind which itself is derived from the Persian word Hindu. This language which developed from the Old Hindi language of Western Uttar Pradesh and Delhi areas exists in two literary standard forms: Modern Standard Hindi and Modern Standard Urdu. The Hindi register itself derives its name from the shortened form Hind linking the language directly to the historical and geographical concept of the land.