In most branches of Hinduism, the soul, or "atman," is separate from the mind, body, and perceptions. Hinduism teaches that we consist of our core of an immortal soul on a spiritual journey. This core is separate from the body, and in fact in most journeys takes the form of many bodies, reincarnating when one physical vessel dies. Hindus consider the world, or maya, a huge bundle of experience leading the soul to the truth. The truth of the soul is that we are all one with God, and every soul of a human or animal is in essence one with God. We are meant to experience and observe the natural world around us, and self reflect and explore our inner selves, to eventually come to the realization that our soul, and every soul, is all the same essence of God. In Jainism, like in Hinduism, the soul is an immortal being separate from the body that reincarnates into a new body after death. Likewise, everything in the natural world has a soul - Jainism largely rests on the fact that even the smallest beings possess souls. However, in Jainism, it is emphasized that each soul is individual and unique, quite the opposite of the Hindu idea that all souls are part of the same whole. Souls can become liberated from the reincarnation cycle to become a Siddha, a God-like being that is all-knowing and achieves infinite bliss.
Although there are similarities in the Jain and Hindu concepts of the soul, they really shouldn't be lumped together. The significant difference of soul independence between the two religions means that they do not define the soul in a similar enough way to be a group. Additionally, Hinduism is a religion with many significant branches that have varying opinions about the soul. Although most include the concept of the atman, the ideas of the sects are so different that they can't all be described under that umbrella term.
[P1] Hinduism and Jainism both define the soul as the immortal essence of a person. [P2] In both religions, the soul is separate from the body and reincarnates into a new one after death. [P3] In both Jainism and Hinduism, every being has a soul. [P4] In Hinduism, every soul is a cumulative part of one God. [P5] In Jainism, every soul is unique and independent.
Rejecting the premises