There are still further connections between the concepts of Buddhism and Hinduism today:
For example, the Buddhist belief in compassion, non-violence, and meditative consciousness has been adopted into modern Hinduism. Likewise, the Hindu tantra or tantric meditations have been incorporated into Buddhist rituals. So, the connection that can be made between the concepts in both religions is that Hinduism and Buddhism share amalgamations of concepts unique to each religion.
Please refer to the links below to read about the connection of tantric concepts in both Hinduism and Buddhism and similarities between varied concepts in both religions.
While it is true that Siddhartha Gautama was raised in a largely Hindu environment, there is some controversy concerning the popular, prevailing notion that Buddhism originated from Hinduism.
Some historians point to the fact that the universal faith of Gautama's background was Vedic in origin. It is supposedly this Vedic religion that is purported to be the main foundation for much of the ancient Hindu faith. These historians claim that the modern Hindu religion has actually experienced an evolutionary transformation through the centuries to arrive at a unique faith structure.
Buddha himself did not relish the cruel practice of animal sacrifice nor the corruption of the Brahman priests within the Vedic religion. He condemned the materialism of the priests and their exploitation of the people and refused to accept the Vedas as the final authority on spiritual matters. Not to be outdone, devotees of Vishnu, the Vaishnavas, taught that Buddha was one of the ten incarnations of Vishnu, but that this valued position served only as an integral test of faith for worshipers. These Vaishnavas claimed that Buddha was chosen as Vishnu's incarnation to test whether devotees would succumb to the false doctrines embodied in the Buddhist faith.
Historians claim that these maneuvers were nothing more than cynical attempts by the prevailing Brahman authorities to maintain their stranglehold on the minds of the people. Indeed, it appears that Buddha was not so much against the Vedas, as he was against what he believed to be a futile obsession with ritualistic ceremonies (such as those practiced by the people under the jurisdiction of the Brahman priests). He vehemently condemned the supreme ascension of the Brahman priesthood to the level of godhood. In Buddha's mind, the priests were largely revered as arbiters of nature's power by the superstitious masses.
Buddha's rationalistic approach is the foundation of his Law of Karma, a cause-and-effect, scientific approach to life. In fact, he points to the Upanishads' (part of the Veda scriptures) assertion that all ritualistic sacrifices and ceremonies are really a form of 'lower knowledge.' Higher knowledge would entail self-realization or enlightenment.
Ironically, the law of Karma has been the foundation of Hinduism since its emergence as a religion. In this foundational aspect, Hinduism's similarity with Buddhism is undeniable. Buddha's criticism of Hinduism, however, originates from his distaste of the Vedic preoccupation with ritualistic, sacrificial worship of anthropomorphic deities. In Buddha's mind, these religious practices threatened to eclipse the rational aspect of Hinduism. Yet, it is important to remember that concepts taught in the Bhagavad Gita (Hindu scriptures) often mirror those taught in the Dhammapada (Buddhist scriptures). For example, Krishna in the Bhagavad Gita taught that worldly pleasures are ephemeral in character, as did Buddha in the Dhammapada.
Krishna: “Those enjoyments which arise through sensual pleasure are wombs of pain, since they have a beginning and an end; O son of Kunti, the wise man delighteth not in these.” (Chapter 5)
Buddha: “He who knows that enjoyment of passion is short-lived and also in the womb of pain is a wise man.” (Verse 186)
To summarize, the foundational similarities between Buddhism and Hinduism are well documented; it is the interpretation of various sects within both religions that has engendered the modern controversies we see today. Despite this, the connection between the concepts in both religions has raised important questions about universal truths relevant to life.
Source: The Development of Hinduism.