Hinduism(sanatana dharma) and Buddhism(dhamma)

Similarities

Hinduism and Buddhism share some of the following similarities.

1. Both Hinduism and Buddhism emphasize the illusory nature of the world and the role of karma in keeping men bound to this world and the cycle of births and deaths.
2. According to the Buddha, desire is the root cause of suffering and removal of desire results in the cessation of suffering. Some of the Hindu texts such as the Upanishads (Isa) and the Bhagavadgita consider doing actions prompted by desire and attachment would lead to bondage and suffering and that performing actions without desiring the fruit of action would result in liberation.
3. Both religions believe in the concept of karma, transmigration of souls and the cycle of births and deaths for each soul. 
4. Both emphasize compassion and non violence towards all living beings. 
5. Both believe in the existence of several hells and heavens or higher and lower worlds. 
6. Both believe in the existence of gods or deities on different planes. 
7. Both believe in certain spiritual practices like meditation, concentration, cultivation of certain bhavas or states of mind.
8. Both believe in detachment, renunciation of worldly life as a precondition to enter to spiritual life. Both consider desire as the chief cause of suffering. 
9. The Advaita philosophy of Hinduism is closer to Buddhism in many respects. 
10. Buddhism and Hinduism have their own versions of Tantra. 
11. Both originated and evolved on the Indian soil. The founder of Buddhism was a Hindu who became the Buddha. Buddhism is the greatest gift of India to mankind.

Differences

Following are some of the differences we can see in the principles and practice of these two religions.

1. Hinduism is not founded by any particular prophet. Buddhism was founded by the Buddha.
2. Hinduism believes in the efficacy and supremacy of the Vedas. The Buddhist do not believe in the Vedas or for that matter any Hindu scripture.
3. Buddhism does not believe in the existence of souls as well in the first cause, whom we generally call God. Hinduism believe in the existence of Atman , that is the individual soul and Brahman, the Supreme Creator.
4. Hinduism accepts the Buddha as an incarnation of Mahavishnu, one of the gods of Hindu trinity. The Buddhist do not accept any Hindu god either as equivalent or superior to the Buddha.
5. The original Buddhism as taught by the Buddha is known as Theravada Buddhism or Hinayana Buddhism. Followers of this do not worship images of the Buddha nor believe in the Bodhisattvas. The Mahayana sect considers the Buddha as the Supreme Soul or the Highest Being, akin to the Brahman of Hinduism and worship him in the form of images and icons.
6. The Buddhists consider the world to be full of sorrow and regard ending the sorrow as the chief aim of human life. The Hindus consider that there are four chief aims (arthas) in life which every being should pursue. They are dharma (religious duty), artha (wealth or material possessions), kama (desires and passions) and moksha (salvation.)
7. Hindus also believe in the four ashramas or stages in life. This is not followed in Buddhism. People can join the Order any time depending upon their spiritual preparedness.
8. Buddhists organize themselves into a monastic Order (Sangha) and the monks live in groups. Hinduism is basically a religion of the individual.
9. Buddhism believes in the concept of Bodhisattvas. Hinduism does not believe in it.
11. Buddhism acknowledge the existence of some gods and goddesses of Hindu pantheon, but give them a rather subordinate status.
12. Refuge in the Buddha, the Sangha and Dhamma are the three cardinal requirements on the eightfold path. Hinduism offers many choices to its followers on the path of self-realization.
13. Although both religions believe in karma and rebirth, they differ in the manner in which they operate and impact the existence of individual beings.

Technically speaking, Hinduism is not a religion but a group of religious and sectarian movements that share some fundamental and in some respects identical beliefs, regional variations, history, tradition and practices peculiar to the land and the times in which they originated and evolved. In contrast, Buddhism is a well established and organized religion having a set of beliefs and practices, commonly known as the Dhamma, based on the Four Noble Truths and the Eightfold Path.
We can safely conclude that in the first few centuries following the nirvana of the Buddha, Buddhism was an integral and significant part of the complex religious character of the subcontinent that was later came to be recognized as Hinduism by the outside world. However subsequently Buddhism crossed the boundaries of the Indian subcontinent and went on to play a much greater role in the whole of Asia. In the process it developed a very complex sectarian, theological and geographical diversity and tradition of its own to become one of the most significant and influential religions of the world. No wonder many people who are not familiar with the history of the Indian subcontinent fail to understand and notice the deep connection that existed between Hinduism and Buddhism in the earlier days and the significant ways in which they enriched each other. 

Buddhism may be considered more as an agnostic religion rather than atheistic. The Buddha's stand on God was rather ambiguous. He maintained silence on the issue of the existence of God and refused to be drawn into any conversation or discussion on the subject, declaring it to be a distraction with no apparent benefit in the liberation of man.