Question
Why is there a separate religion for Buddha, if Buddha is a Hindu god?
Answer
It is because the discrimination of religions as it has come to be is mostly based upon the primary scripture or teachings of the prophet or god rather than who the god is or who the proponent is.
So irrespective of whether Buddha is a Hindu god or not, the message he preached and spread is different than that of Hindu/Vedic beliefs. For example while Hindus, who accept the authority of the Vedas, believe in the existence of individual souls and a Supreme God, the Buddhists do not. Buddha did not accept the authority of the Vedas and spread a tenant opposite to it shunning yajna, animal sacrifice, etc. So due to the difference in the core beliefs it has come to be known as a separate religion having its own sub-sects over the course of time.
However, having said that I would also like to say Buddhism, Jainism, etc. were considered as different philosophies and schools of thought rather than separate religions. They belong to the nastika (heterodox) schools of thought in Hindu Philosophy. These schools of thought came to flourish in India where there were no such thing as religion as that term means today. Even there is no word for religion in Indian languages and it is commonly translated as dharma which can mean many different things depending upon the context. Only in course of time as other religions started to flourish in different parts of the world that the distinction became more. So even if Buddhism is considered and categorised as a separate religion, many would agree (and of course some wouldn't) that it is just a different darshana (philosophy) and way of life.
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