Adwaita which advocates non-dualism states that there are no two separate entities as Jeevatma or Paramaatma. There is only one indivisible paramaatma. Adwaita philosophy believes that there is only one entity (God) that is truly existing and all other variations (whether sentient or non-sentient) we see are our perceptions which are mistaken of only one as many. Adwaita means “no second”. The Advaita philosophy was propagated by his holiness Shri Sankaracharya, who based his theories of Advaita on the Upanishads and teachings of his Guru, Shri.Govinda Bhagavadpada. Shri Sankaracharya exposed the relative nature of the world and established the non-dual reality of Brahman in which Atma (individual soul) and Brahman (the ultimate reality) are same. Sri Sankaracharya was also famous for denouncing meaningless rituals. The paths of raja yoga and jnana yoga are associated with Adwaita.
Dwaita philosophy on the other hand was propounded by his holiness Madhwacharya in the 13th century. Dwaita philosophy proclaims that god and souls are different entities. Dwaita philosophy is opposed to the Advaita philosophy of Sankaracharya which believes in non-dualism. According to the Dwaita philosophy, souls are eternal but are not created by God, as in other systems of religion. According to Madhwacharya, souls belonged to three different classes, Mukti-yogyas, Nitya samsarins and Tamo yogyas. The differences between Adwaita and Dwaita can be best explained through an example:
According to Dwaita – Wave is different from the ocean.
According to Adwaita – Wave and ocean are one and the same in essence i.e. water. It says that neither the ocean nor the wave can survive without the water. Wave is just a small part of the ocean and Ocean is the sum total of everything. When seen transcending the individual and total it is just the water that pervades all the waves and the ocean. Infact, when the individual is transcended and has been identified with water, the totality is also automatically transcended. Dvaita follows the preachings of Advaita, both enter the same destination, however, have different paths while entering it.