There are so many layers to this in terms of spirituality, religious identity, political machinations, and the notion of defining religions in general, that any chance at simplicity is lost.
From the outset, I think that some basic principles need to be articulated. Many in both religious communities as well as basic scriptures in Hinduism, known as the Puranas, do recognize that Lord Buddha as an avatar of Lord Vishnu. This avatar predates the one driven by wordly sin into a rage of destruction. The Gautama Buddha is seen as a force of enlightenment. The beliefs of this vision of Vishnu represent the totality and desire for liberation as traditional Hinduism. There are some distinct differences, though. This version of Vishnu does not advocate the role of creator Gods, something vastly different in traditional Hinduism. This avatar also stresses the idea that suffering comes from attachment, something that is intimated in Hinduism, but not always deliberately articulated in such a manner. The lack of social stratification is another noticeable difference between both sets of thought. Yet, the same fundamental ideas of locating spirituality within the individual and striving to achieve a liberation out of this life into another one is present in both religions.
The issue of where the early belief system originates in Buddhism is a very sensitive one. There are some who argue that both religions essential preach the same thing. Thinkers like Swami Vivekananda and Radhakrishnan argue that there is a universality of religious expression that both Hinduism and Buddhism stress. The political dimension here is apparent as these assertions could be a response to Christian proselytizing throughout India and in arguing that Hinduism embraces a universality that other religions fail to, a motive of primacy can be given to Hinduism with its connection to Buddhist origins and beliefs. Some argue that the Lord Buddha was not an avatar of Vishnu, striving to make distinctions between both religious forms of worship. These individuals make the argument that the lack of rituals and practices in Buddhism are not consistent with Lord Vishnu and the devotions and oblations that are to accompany his worship. Others argue that both religions did have different belief systems, but the presence of Lord Vishnu as an avatar of Buddhism was a political move calculated by Hinduism to coopt the rising interest of Buddhism, inspired no doubt by Buddhism's disavowal of the caste system stratification. In this, one finds a level of complexity in the idea of whether or not there were beliefs that were overlapping or "the same" in both religions.
In the end, I am not sure where to go because I would never pretend to be any voice of religious authority. I do think that it is important to hallmark differences in religious worship, but recognize that Swami Vivekenanda might have been fairly close to getting it right in his evaluation of the issue of "sameness" between both religions:
May he who is the Brahman of the Hindus, the Ahura Mazda of Zoroastrians, the Buddha of Buddhists, the Jehovah of the Jews, the Father in Heavens of Christians, give strength to you to carry out your noble ideas!
Like so much in spiritual worship, Swami Vivekananda has a way of making complexity into "understandability."
Yes, the beliefs of early Hindus and Buddhists were fundamentally the same. Both religions originated in India and are closely related. The Buddha was born in a Hindu family, just like Jesus was born in a Jewish family. Many believe that Buddhism was an offshoot of Hinduism. The two religions have several similarities:
The role of karma in keeping men bound to this world the cycle of births and deaths desire is the root cause of suffering the removal of desire results in the cessation of suffering transmigration of souls compassion and nonviolence towards all living things the existence of several hells and heavens the existence of several deities practices of meditation, concentration, and cultivation