It is not possible for me to go into detail into each of the schools, so giving just a brief overview in layman's terms here. If you need a deeper understanding, would recommend you to study the philosophies in depth.
Vedanta in a literal sense is "End of the Vedas" which basically refers to the appendix to the Vedic hymns and in a deeper sense, mastering the end goal or purpose of the Vedas. While it was used to refer to Upanishads in the early period, later on during the medieval period, it came to mean the interpretation of the Upanishads. While there are many schools of the Vedanta, all of them seek to answer the basic question, the relation between the Atman (Inner Self or Soul) and Brahman and that between Brahman and the World. It is the various answers to these questions that have come to form some of the more well-known schools.
These schools have certain basic concepts
Brahman is the supreme cause of the entire universe and is eternal and all encompassing.
All actions are subordinate to knowledge and devotion.
Bondage is subject to Samsara, the eternal cycle of death and rebirth.
And deliverance from the cycle of Samsara is true liberation.
Now going by the classification we have the following schools
Advaita-
This is the oldest school of Vedanta, and it states that Brahman is the only reality and the world is illusory (Maya). Ignorance of the reality is what causes suffering, and liberation can be obtained only by true knowledge of Brahman. It states that both the individual self (Atman) and Brahman are the same, and knowing this difference causes liberation.
The philosophy of Adi Shankaracharya AKA grand monism - According to Shankara, the ultimate reality viz Brahman is pure consciousness and without any attributes. Brahman is Nirguna. Jivatma or souls is a subject-object complex on account of avidya (ignorance) fancied by maya. Liberation is possible only through Jnana. For Shankara, Karma is only a subsidiary and rejects Lila as a reason for creation. Shankara considers the world to be Mithya or rather an unreal manifestation of Brahman. This is known as Brahma-Vivartavada. But this 'idea' of 'Mithya' is also on account of Avidya. Hence the three states of consciousness such as Waking, Dreaming, Deep sleep never really take place but only seemingly happen due to ignorance. Once Brahma Jnana dawns, there would neither be a waking or a dream. The world is not at all there and there is no ignorance also (except hypothetical) second to the really real brahman.
Dvaita-
This was propounded by Madhvacharya and is also called as Tatvavada- the Philosophy of Reality. It considers Brahman and Atman as two different entities, and Bhakti as the route to eternal salvation.
According to Dvaita, Jivatmas are many and Paramatma is one. There are 'n' number of souls and each soul has different characteristics and modes. Difference is the very nature of all things. Souls are dependent on god and god is the creator, preserver, destroyer of the universe. He has a divine body and is transcendent. He is also the immanent ruler of all souls. He damns some and redeems some others. He is the lord of Karma. He is pleased only by Bhakti. He manifests himself as various avatars and is present in images.
Concerning the soul, Madhava says that no two souls are alike. They each have different characteristics, different states of happiness/sorrow...the soul becomes similar to god in some respects when it is liberated, yet even in these respects it is much inferior to god. It does not enjoy the full bliss of God. The bliss enjoyed by the redeemed souls is fourfold:
Salokya - residence with the same place with god
Samipya or nearness to God
Sarupya - Having the external form like that of god
Sayujya - Entering into the body of god and partially sharing his bliss
According to Madhavacharya, even the most qualified soul which is entitled to Sayujya form of liberation can share only partial bliss of Brahman and cannot become anywhere similar to Brahman.
Further, Madhava believes that certain souls like asuras i.e, demons, ghosts and some people are eternally doomed and damned. They can never hope to get liberation. Madhavacharya's philosophy is known for its extreme gradation, hence I have referred to it as Pure Dualism. The authority for such gradation is not to be found in the Vedas and it appears that Madhavacharya was quite given to flights of fancies
Bhedabheda-
As the name suggests it looks at the concept of difference (Bheda) and non-difference (Abheda). This school states that the jivatma (individual self) is both different as well as similar to the ultimate reality Brahman. In a way this combines both the teachings of Dvaita (which states Individual Self and Brahman are different) and Advaita (which states that both Individual self and Brahman are one and the same). This school was particularly popular during the medieval era, with thinkers like
(1). Ramanuja (who pioneered Vishishtadvaita),
(2). Nimbarka (founded Dvaitadvaita),
(3). Vallabha (Shudadvaita) and
(4). Chaitanya Mahaprabhu (founder of Gaudiya Vaishnavism)(Achintya Bheda Abheda)
(1).Vishishtadvaita-
Literally meaning the Unique Advaita, this was pioneered by Ramanuja during the 11th century. While it accepts Brahman as the unified whole, it states he is characterized by multiple forms. In a sense it believes that all diversity is subsumed to a unified whole. It's philosophy is summed as up Asesha Chit-Achit Prakaaram Brahmaikameva Tatvam meaning Brahman as qualified by sentient modes (the ability to feel and sense) and insentient modes (inability to feel or sense) is the only reality.
It is qualified Monism that is, advaita with some amendments. I have asked many Iyengars as to how monism can be qualified and still retained. The answers have been very deflating though. Further, the name itself appears contradictory. Is it Vishist-advaita or Vishista- Dvaita?
According to Ramanujacharya, souls are intrinsically the same and all souls are alike in their quality. Bondage is ascribed to beginningless Karma. God is identified with the absolute and brahman is savishesa or a qualified unity. God stands for the whole universe and matter and souls form his body, he being THEIR soul. God is viewed as the cause and also as the effect. During pralaya, god remains as the cause with subtle matter and unembodied souls forming his body. The whole universe lies latent in him. During creation, the subtle matter becomes gross and the unembodied souls become embodied according to their karmas. Ramanuja distinguishes these two states as "state of cause" (Kaaranavastha) and "state of effect" (Kaaryavasta) of Brahman.
Souls are classified into three by Ramanuja
1) Nitya Muktas - souls which were never bound - they are ever free from karma and prakrti and live in vaikunta in constant service of the lord. Adisesha, Garuda, Visvaksena etc are some such souls
2) Mukta Atmas - Souls who were once bound but who obtained liberation through action, knowledge and devotion.
3) Baddhatmas - Souls who are wandering in samsara on account of ignorance and bad karmas.
Ramanuja's philosophy is a fusion of the vedas and the bhagavad purana. He was enormously influenced by the Tamil Bhakti Saints called Alvars.
(2). Dvaitadvaita-
The philosophy of Nimbarka is an offshoot of vaishnavism. Propounded by Nimbarka, it states that the Brahman is the highest reality, the controller of all. And is also the cause of creation of the Universe. The Chit or Jiva, the individual soul is which posseses both the knowledge and is knowledge itself. In a way similiar to the sun which is both light as well as the source from which all light comes. Achit or Jagat is basically of 3 sorts- Prakrta( derived from basic matter), Apkarta is that which is non Prakrta and Kala. It states that Brahman or Isvara, is the highest reality and both Chit, Achit are dependent on him.
Nimbarka very much agrees with Ramanuja and admits the three realities, god, souls and matter. Soul and matter are dependent on god. The nature of the soul is knowledge itself. The soul is atomic in size and are many in number. A soul is eternal and yet suffers from births and deaths on account of its embodiment due to karma and avidya. Liberation is due to knowledge which is brought about by God's grace which itself is due to devotion. Hence according to this school of thought, bhakti is the only means for liberation.
(3).Shuddadavaita-
Pure non dualistic form of philosophy, propounded by Vallabhacharya. As per this, both God and the individual self are the same, and not different. However it differs from Shankara's Advaita, in that considers the individual self as part of God who is the whole. It also states Maya is not unreal, unlike Advaita, but a manifestation of God's power.
According to him, Brahman is an independent reality and is identified with Krishna Paramatma whose essence is existence, knowledge and bliss. Souls and matter are his REAL manifestations and all are his parts. He is the epitome of all good qualities. Salvation is possible only through loving service of god. Though Vallabha accepts that the soul is bound due to ignorance, he believes that knowledge is possible only through divine grace.
(4). Achintya Bheda Abheda-
This was enunciated by Chaitanya Mahaprabhu, the founder of the Gaudinya Vaishnavism. It combines both the views points of the Advaita and Dvaita schools. It states that while the individual self is linked with Brahman, yet it is not the same as him. It states that the individual self is only a part of the Supreme Lord. In a sense it breaks away from the rather rigid definitions of Dwaita and Adwaita.
Summary: According to Ramanuja, the soul though different from god is essentially identical with him as forming his body. For Madhwa, the soul, though a dependent part of god, is essentially different from him. As per Nimbarka. the soul is limited and dependent and is different from god, though it is identical with him. For Vallabha, the soul is a part of god and is identical with him and appears as different on account of limited manifestations.
All the above schools of thought holds creation to be a REAL phenomenon except for the Advaita which declares that creation to be a UNREAL .
