Bharat, India and Hindustan are the three names that refer to the country of India. They differ in terms of the times of their origin, importance, significance and the like.
There is indeed a different semantic meaning attached to each of the three words, namely, Bharat, India and Hindustan. India and Bharat are used in the two official languages, namely, English and Hindi, and the word Hindustan is used in a popular way.
The word Hindustan might have originated from the sentiments shown by the citizens of India that believed that the land belonged primarily to the Hindus. Hence there might have been a political thought involved in the formation of the word Hindustan; Hindu flavor is reflected in the usage of the word Hindustan.
The word Bharat would have originated in the times of King Dushyanta of the epic period. Duhsyanta and Shakuntala were blessed with a son by name Bharata. India would have been named Bharata based on the name of the son of Duhsyanta who also had the same name.
Some people believed that India is the seat of classical music and hence the word Bharata referred to Bhava (bha), raga (ra) and tala (ta). It is important to know that all the three, namely, bhava, raga and tala are vital in classical music.
The word India would have come into existence in the course of time from the development of the word ‘Sindhu’ or the River Indus flowing in Punjab. The word Indus might have developed into the word India as centuries went by. It is interesting to note that the word Hindustan might have become all the more popular after the composition of the song ‘saare jahan se accha’.