Hinduism, or Sanatana Dharma (eternal law) that has no founder or church, is one of the oldest religions in the world. With its billion followers, it is actually the third most widespread religion after Christianity and Islam. While the origin of Hinduism comes from the Indus civilization (Sindhou), around III millennium B.C., its recent form comes from the Vedic period, 1500 B.C.
Hinduism has the peculiarity of having no prophets and no central dogma. However, contemporary Hindus believe in the authority of Veda, which, according to the tradition, was revealed to mankind thanks to the Rishi's vision. As a matter of fact, the religion is a set of philosophical concepts from the Indian proto-history. This religion assimilated beliefs and philosophies from numerous conquests and invasions on the Indian subcontinent. Consequently, Hinduism evaluated a lot through time.
Buddhism is a religion, a philosophy, or both, whose origins date back to V B.C. after the enlightenment of Siddhartha Gautama. With half a billion followers, it is the fourth most widespread religion after Christianity, Islam, and Hinduism. It gathers a ramified set of meditative and ethical practices, psychological, philosophical, cosmogonic, and cosmological theories addressed in the perspective of Bodhi "Enlightenment".
Even though Buddhism is commonly perceived as a godless religion, the cult of the historical Buddha (Siddhartha Gautama) as a Bhagavan plays an important role in the Theravada and particularly in the Mahayana, which is giving him the rank of demi-god.
Just like the Jainism (and unlike the Hinduism, which instigated the Brahamic tradition), Buddhism instigated the Shramana tradition.
Jainism, from the Sanskrit Jina "Winner", is a religion insisting on the respect of the Ahimsa (non-violence), and based on the theory of karma, reincarnation, and ecology while focusing on asceticism. It doesn't have its roots on Hinduism (unlike Buddhism), but it is one of the oldest religions in the world (3000-3500B.C.) under the influence of Mahavira. Nowadays, the number of followers of Jainism is almost twelve million from around the world.
Given that Hinduism and Jainism have not left their traditional sphere of influence, that is to say, India; it is clear that social and religious aspects of life of the Jains and Hindus may seem quite similar to a westerner. But if one is committed to carefully compare those two great philosophical currents, we could quickly discern our error.
At first, the Jains do not accept the sacred Hindus' books (Veda, SmRi, Purama), and the Hindus do not recognize any Jainism writings; then comes their idea of the universe. The Jains think it is eternal and naturally confronted to infinity of cycles while Hindus believe that it has been created and submitted by multiple cycles that are generated by gods, themselves necessarily generated by cycles.
The Jains worship those who conquer their supreme ideal, and arrive to the divinity by themselves. On the other hand, Hindus believe in other forms, incarnations, or avatars of one god, creator and master of the universe.
The path of the salute in Jainism is simple and unique, decomposed to three "jewels" that can be followed by all. One's capacity and motivation depend on the accumulated karma during one's life. Hinduism offers many ways generated by different Guru, or spiritual masters.
The Jains consider karma as a special form of matter that can be incorporated into the soul, being some kind of link between the spiritual, immaterial, eternal soul, and the body, while the Hindus estimate that karma is an invisible power completely equated with the soul.
Regarding the religious practices known in Hinduism like worshiping of trees, cow tails, and rivers, those practices are considered as superstitions (mudhata) by the Jains, and are better avoided.
Whereas Jainism and Buddhism have some points in common, like the fact that Vedas, sacrifices, and caste systems aren't recognized by either of the two religions, they do have fundamental differences.
Jainism is an atmavadi religion, conceived from Jiva (eternal and individual soul). On the contrary, Buddhism, which is an anatmavadi religion, rejects every idea of a soul. Although the "golden rule" of Buddhism is non-violence, it does a more limited use of it than Jainism.
Lastly, Jainism is an ascetistic religion that attaches importance to austerity and penitence. In Buddhism, the rejection of asceticism by the Buddha during his path to enlightenment is one of the events that allowed determining "the middle way".
According to the Buddha and his four noble truths, the human's problem is suffering (also known as ignorance) caused by the pleasures of life which do not last forever. Buddha's solution to overcome human's problem is asceticism, renouncement all the illusory pleasures of life, and finding a source of lasting satisfaction through meditation on ones way to enlightenment.