Short answers, pulled from the story.
Hindustan is the Persian-language name for India, broadly the Indian subcontinent, with Hind as its shortened form. The word later became commonly used by India's own inhabitants in Hindustani, and its Arabic equivalent is al-Hind.
Hindustan derives from the Persian word Hindū, which is cognate with the Sanskrit word Sindhu, meaning Indus River. The suffix stan, meaning country or region, was added around the first century CE to form Hindustan.
In 515 BCE, Darius I annexed the Indus Valley, including present-day Sindh, and Persian speakers called that region Hindu. By 262 CE, an inscription of Shapur I at Naqsh-e-Rustam already used the term Hindustan for Sindh.
Indian leaders objected because Hindustan implied the land of Hindus specifically, and they wanted the new dominion called India instead. As a result, Hindustan never received official sanction from the Constituent Assembly of India, while Bharat was adopted as an official name.
Muhammad Ali Jinnah, the founder of Pakistan and leader of the Muslim League, insisted on calling the modern Republic of India Hindustan, in reference to its Hindu-majority population.
Under the Delhi Sultanate (1206-1526) and the Mughal Empire (1526-1857), Persian historiographers of the ruling elite used Hindustan for the Muslim-controlled Doab and nearby northern territories, while Hind referred to the rest of India. The Mughals themselves called their own lands Hindustan, and as their empire expanded, so did the territory the word was taken to cover.