Hinduism is Sanathana dharma, the ancient teaching, sometimes called the perennial philosophy. Hinduism has different forms of practice, and different philosophies; there are three main schools, and three main devotional paths.
Buddhism is both a way of life and a philosophy - some would call Buddhism a religion, others not. If the Buddha could be proved to have not existed, then there are Buddhists who say that the philosophy, the way, (called the middle way) would continue. Hinduism, for example, considers Buddhism a religion and Buddha is one of the avatars of Hinduism.
Buddhism differs from Hinduism both by practice and philosophy; the four noble truths point right mindededness and practice, the goal of which is extinction or cessation of the round of birth-rebirth. Buddhism does not need God nor any other Gods, although there are schools of Buddhism that have Gods. Hinduism, on the other hand, has multiple Gods, and finally, the goal is non-dualism, jivan-mukti, realising you and God are no different. Theravada Buddhism believes that the Buddha is a teacher. Mahayana Buddhism believes that the Buddha is a god.