Historically the Indus valley saw the Vedic religion thrive. In the time when the Veda’s were developing into what many call Hinduism the Buddha was teaching for what would become Buddhism. This is what happened from an outside view. From within Buddhism developed as a part of the Vedic tradition and was never necessarily separate from what would become Hinduism. This is evidenced in the fact that Buddhism no longer resides in the place of its birth.
Philosophically Hinduism and Buddhism are similar in their stark differences.
One of their vast nearly undeniable similarities is their ontological conceptions. Both systems are based on the illusory nature of the physical world. Some sort of error or miscalculation occurs in the human perception.
In Hinduism one is to understand Brahma or existence from within their own Atman, roughly soul. The highest life is a process of removing the bodies distractions from life, allowing one to eventually understand the Brahma nature within. The physical world is a representation of actual existence.
In Buddhism we find the Anatman or not soul, but might be best understood as the antithesis of the Atman concept. In Buddhism one follows a disciplined life to moved through and understand that nothing in ourselves is ‘me’ such that we dispel the very illusion of existence. In so doing one realized Nirvana. This realization is presented as the understanding that no beings exist in this world as much as all being exist in the ‘paradise’ existence free Nirvana.
I think it is safe to say that both are monist in nature. Both ‘endorse’ or see ontology as a single unified thing. Each sees all beings as a part of this unity. Each are accepting of all life paths and though they survive on their population of monks do not require or even ask people to change their lives. Both see existence or life within the framework of reincarnation and karma.
They are vastly difference in their theological aspects. Hinduism is rich with gods, embracing the animistic gods previous to Vedic intervention on up to the pantheon most often presented as Hinduism. In essence Hinduism has as many gods as people have a need to think up, though all are a single Ishtar or manifestation of Brahman.
Buddhism on the other hand rejects metaphysical proclamations in so far as it warns against the nature of becoming attached to metaphysical ideas. For this reason Buddhism is often called atheistic.
