The president is the head of state, whereas the prime minister is the head of government. A college of electorates determines the president, but the president selects the prime minister from whichever party carries the majority in the lower house of the parliament, called Lok Sabha. The United States is a big democracy in the world.
It is comprised of a presidential republic, and the president has the ultimate power, aside from the system of checks and balances that are in place. There is no prime minister of the United States. There are other places, for example, in which the president appoints a prime minister, such as France. In other countries, the prime minister is the head of state, such as The House of Commons in England.