This has been in existence for few centuries. There are 18 philosophical / interpretational differences. As they are niceties of each sampradayam, it would require atleast 3 years of study of both to appreciate the differences in the right way. So it won’t be meaningful to just list them here. I would also suggest you to follow the one that you belong to rather that getting into the differences. If you have already spent enough time in knowing each sampradaya, then I can suggest books that list the differences.

Sri Ramanuja Munaye Namaha,

Asmadh Sarva Gurubhyo Namaha,

Sri Velukkudi Krishnan Swami Guruve Namaha,

Dear BhagavatA,

By this time in 2 years after posting the question, adiyen believe, BhagavAta would have already known the answer from Upanyasams, but adiyen is sharing only for other/those Bhaktas to understand about Thayar Perumal and the 3 Tatvams, based on Swami’s Pravachanams, so that they could get Thayar Kataksham first for Moksham, instead of debating which Tattvam is Sri MahaLakshmi and what is Vadakalai and Thenkalai, when we all are under same shade of Swami Ramanujar.

*******************************

Here are some references from Swami’s Pravachamnas and Acharyas Vaarthaigal regarding:

1) “Sri MahaLakshmi Thayar which Tattvam”, and

2) “Thenkalai-Vadakali with in Swami Ramanujar Dharishanam”.

[Caution: Those who read with “Open Mind and Patiently” will understand what is being said by Swami & PoorvAcharyas based on Shastras. And those who read with “Preconceived mind” trying to Insert their own abhimaana demi-gods into the Shastric Arthams as they are also another tattvam which Shastras doesn’t say, will not understand what is being said by Swami & PoorvAcharyas, and we don’t need to satisfy their own thinking or interests].

Below is not adiyen’s explantion, but what Swami & Poorvacharyas have said, So adiyen would like to share the same based on adiyen’s understanding from Upanyasams.

Sri Velukkudi Swami to forgive adiyen for any errors and bless aidyen further.

************************************

A) One Reference,

During “Kainkarya Srimaan” award function at chennai, which was A great wonderful effort and service by our ” Upanyasa Sigaram” Velukudi Sri.U.Ve. Sri Velukkudi Krishnan Swamygal arranged by Kinchitkaram Trust in 2014,

Jeer Swamigal Sri.U.Ve Embar-Swamygal-Sriperumputhur (Thenkalai) and Sri.U.Ve.Azhagiasinger Swamygal-Ahobilamadam-46th pattam (Vadakalai), were present and graced the function.

Embar Jeer Swami beautifully says @ 14:05 minutes in below youtube,

“Nammudaya Sampradhayathil Sriman NarayanAn Arul Seikiraan. Ramanujar adiyargal Vishayathula Tatva Bhedhame kidayadhu Yochana Bhedham Ozhiya”

“நம்முடைய சம்பிரதாயத்தில் ஸ்ரீமன் நாராயணன் அருள் செய்கிறான், ராமானுஜர் அடியார்கள் விஷயத்துல தத்வ பேதமே கிடையாது, யோசனை பேதம் ஒழிய “

(Only “Yochana Bhedham” & “NO Tatva Bhedham”)

https://www.youtube.com/watch?v=k2xRVK1yy60

Both Kalai’s,

1) DON’t have any “TATTVA Bhedham” (No difference is Tatvams, both accept ‘3 Ttavams’ (Countless Chit’s, Countless Achit’s, ONE ParamAthma Sriman NarayanAn)

2) Only “YOCHANA Bhedham” (difference in thought process only for BhagavAt anubhavam till we leave this Prakrutha Shareeram).

*****************************

Three Tatvams as per Shastras (Tatva Trayam):

“Yasya Athma Shareeram Yasya Pritvi Shareeram” –> Upanishadh Vaakyam.

(All Chit ‘Athma’ & All Achit ‘Pritvi’ are body ‘Shareeram’ for Sriman NarayanAn).

1) ParamAthma (ONE) –> Sriman NarayanAn

2) Chit (Countless) –> Sentient, Uyir Ulladhu, ALL JeevAthmas.

3) Achit (Countless) –> Insentient, Uyir Attradhu, ALL Jada Porulgal.

****************************

B) Another reference,

Sri Velukkudi Krishnan Swami beautifully says, How Tatvam is common (No Tattva Bhedham) for all as per Shastras, and How there is Yochana Bhedham (Difference in thought process) as follows:

Breaking down the ‘ParamAThma’ பரமாத்மா word.

பரமாத்மா = பரமன் + ஆத்மா.

1) ‘பரமன்’ means ‘ப்ரோமா அஸ்மாதிதி பரமஹ’

‘Paraman’ means ‘Paroma Asmaathithi Paramaha’

[‘Paraman’ means, “Ivanai Kaattilum Mein Pattavan Yaarum Kidayadhu, Samamm Aanavanum Yaarum Kidayadhu’, NO one Higher or Equal to HIM, ALL are Below HIM only”].

2) Breaking down ‘Paraman’ ‘பரமன்’ again as ‘ப + ரம’ (Pa + Rama), not pronounce as Raama ‘ராமா ‘, just Rama ‘ரம’.

ரம’ ‘Rama’ means Sri Maha Lakshmi Thayar as per Shastras.

பர ‘Para’ means Sriman NarayanAn as above ‘Paraman’ meaning, when added to ரம ‘Rama’ (Sri lakshmi), it means, ‘ ‘பரமன்’ means Sri Lakshmi Sambhamdham UdayavAn.

3) ஆத்மா ‘Athma’ means Sentient, Uyir Ulladhu in general.

So, பரமன் (‘பர’ Perumal + ‘ரம’ ‘SriLakshmi) + ஆத்மா = பரமாத்மா = Divya AThma = Divya Dambhathi. So Unqiue & only ONE compared to the countless Athma (Chit), and NOT applicable to any other Jeevathamas whether in Human body or Deva bodies (Brahma , Shiva etc…) or any bodies.

********************************

Another way to say is,

PARAMATHMA “பரமாத்மா” word is divided as “PARA + MA + ATHMA.

* PARA means Param Porul NarayanAn.

* MA means “Jagadh’MA’tha. Yella JeevAthamaakka’lukkum THAYAga Iruppaval.

* ATHMA is Chit ‘Sentient’ CHaithanyam Udayadhu.

So, ParaMAthma word is NARAYANAN and THAYAR Inclusive is one meaning.

Hence we call as “SRIMAN NARAYANAN”, and we don’t seperate Thayar from Perumal as Thayar Resides in Perumal’s Vaksha Sthalam (Thiru MAarbhu all the time).

****************************

This is called as “Yochana Bhedham” but “No Tattva Bhedham” as per Shastras, since Swami Ramanujar has said only 3 tavamas and we Both Vadakalai and Thenkalai are sub-sects of Swami “Ramanuja Dharishanam“, since Swami Vedanta Desiakr didnot create any Vadakalai and Swmai Pillai Lokacharyar/Swmai Manavaala Maamunigal didnot create any Thenkalai. Later in recent centuries Abhimaanis of these Acharyas created a Kalai for their own following and named the existing as another Kalai, but the core Sampradhayam is “Swami Ramanuja Dharishanam” that all Acharyas followed, which is what we should be following, since we all are JeevAthmas Servant of ParamAthma Sriman NarayanAn”

***********************

Hence, when we deal with Perumal & Thayar, it is abvious that, some quickly, say Sri Lakshmi Thayar is one of JeevAthma like other Countless Chit, but who understands well that we BhaddhAthmas (Athmas trapped in Samsaram like us) inorder to go to Moksham ‘SriVaikuntam’, we need Thayar Purushakarathvam (Kataksham) first, then only NarayanAn will grant Moksham. Hence we call as “Sriman NarayanAn” or “SriyaPathi” means, Perumal is identified as Husband (Pathi) of Thayar (Sriya). So Thayar is more important due to her Karunai ullam. Thayar always in NArayanAn VAksha Sthalam “ThiruMaarbhu/Chest’ (Vittu Piriyaamal Iruppaval/not even seperate for a fraction of a second).

Perumal THe SUPREME ParamAThma is identified as “SRIYA PATHI” (Husband of Sri Mahalashmi). Hence, without Sri MahaLakshmi, Perumal is NOthing.

***********************

Examples of Sharanagathy:

1) Swami NamAlwar did Sharanagathy on Thayar-Perumal ThiruvAdi as

NamAlwar says in ThiruVaiMOzhi 6.10 says about Piratti Thayar as:

agalikillEn iraiyum endru! AlarmEl MangAi urAimaar’bha,

nigharil pugazhaai! ulagam Moondrudaiyaai! yennai aaLvaanE,

nigharil amarAr munikkaNangaL! virumbhum thiruvEnkadaththaanE,

pughazh ondrum illaa adiyEn! uN adikkeezh Amarndhu pugundhaeNae.

Swami says Meaning in short as,

பத்மாவதி அலர்மேல் மங்கை தாயார் அவர்களை, தன் திரு மாரபில் கொண்டு இருக்கும் திருவேங்கடத்தவனே,

உலகத்துக்கு எல்லாம் அதிபதி ஆன பகவானே, என்னையும் எப்போதும் ஈசனாக இருந்து ஆளக்கூடிய எம்பெருமானே ,

உனக்கு சமமாக புகழ் படைத்தவன் வேறு யாரு, உனக்கு சமமானவனும் இல்லை, மேன் பட்டவனும் இல்லை, தேவர்கள் ரிஷிகள் ஆகிய அனைவராலும் போற்றும், எல்லாராலும் ஆச்ரயிக்க படும் திருவேங்கடத்தானே,

எந்த புகழும் இல்லாத அடியேன், உன் திருக்கடி தாமரைக்கு கீழ அமர்ந்து, உன் திருவடியை அடைந்து, பத்மாவதி தாயாருக்கும் உனக்கும் கைகர்யம் செய்தெனே.

2) Swami Ramanujar Did Sharanagthy on SriRanga Nayagi Thayar & SriRama (Namm PErumal) Lotus feet on Panguni Utthiram in SriRangam and further asked Moksham for all of HIS SAMBHANDHIS like us as written in “Sharanagathy Gadhyam”.

**************************************

Please listen to Swami’s Enpani #735 “Sri MahaLakshmi As Explained Swamy Alavandar”.

https://www.kinchit.org/kinchit-en-pani/701-750/

Sriman Narayanan (SriKrishna) has KARUNAI (Mercy) but covered with Kopam (ANGRY) seeeing our PAAPAM (SINS).

Swami says, when we go infront of Perumal Directly, then there is possiblity that Perumal will look at our Paapam and may punish. So Sri MahaLAkshmi CORRECTS our mistakes and make us ELIGIBLE to get Perumal blessings. THis is called as PURUSHAKARATHVAM by SriLakshmi PIratti (Recommending to Perumal to forgive our Paapams as we are HIS Child).

Hence, by doing Acharya SHaranagathy (Surrendering ourselves ‘ATHMA SAMARPANAM as ADIYEN is Property of BOTH PIRATTI_THAYAR and PERUMAL and NOT a property of ANYONE ELSE/ Demi-Gods), then we get Piratti Thayar-Perumal (Sriman Narayanan) blessing for ATHMA UJJIVANAM by GETTING SWAMI RAMANUJA SAMBHANDHAM.

So, Lets keep chanting daily the slokam as Swami says in Enpani #735 and get out of this BIrth DEATH cycle from this Janma itself.

“Lakshmi Naatha Samaarambham, Natha-Yaamuna Madhyamaam,

Asmadh Acharya Paryanthaam Vandhae Guru Paramparaam”.

லட்சுமி நாத சமாரம்பாம் நாத-யாமுன மத்தியமாம்

அஸ்மாத் ஆச்சார்யா பர்யந்தாம் வந்தே குரு பரம்பராம்

*************************************************

C) Another Reference,

There are also other references in this link referring to Swami’s Upanyasams regarding the Bharanyasam (Vadakalai) & Panch Samskaram (Thenkalai). Both are basically getting Swami Ramanuja Sambhandham for Moksham and both do Prapatthi.

• Vadakalai does Panchasamkaram and Prapatti at two different times depending up shisyas interest,
• Thenkalai does Prapatti & Panchasamkaram at same time during Samasrayanam.

https://www.kinchit.org/dharma-sandeha/thread/bharanyasam-vs-pancha-samskaram/

****************************************************

Thenkalai & Vadakali, both get Moksham “SriVaikuntam’ through JagadhAcharyar “Uddharaka” Swami Ramanujar. So, Kalai Bhedham (difference in Kalai’s) is ‘NOT Tatva Bhedam” (No Difference in Tatvam, both accept 3 tatvams Chit, Achit & one ParamAthma Sriman NarayanAn), since both follow common “EmperumanaAr (Ramanujar) Dharishanam”. And all BhaddAhtmas either in ordinary Human bodies like us or Hi-Fi Deva bodies like Brahma, Shiva, Indra, etc…ALL have to get SriMahaLakshmi Thayar PurushaKaarathvam (Kataksham) and finally reach SriVaikutam to do Nithya Kainkaryam for Divya Dhambhathis which is Nithya Anubhavam.

************************************

Again,

[Caution: Those who read with “Open Mind and Patiently” will understand what is being said by Swami & PoorvAcharyas based on Shastras. And those who read with “Preconceived mind” trying to Insert their own abhimaana demi-gods into the Shastric Arthams as they are also another tattvam which Shastras doesn’t say, will not understand what is being said by Swami & PoorvAcharyas, and we don’t need to satisfy their own thinking or interests].

***********************************

Namakku Yellam Sath Gyanatthai Ootum Sri Velukkudi Krishnan Swami ThiruvAdigalaey Sharanam.

Adiyen Sri Velukkudi Krishna Dasan,

PoorvAcharyargal Thiruvadigalaey Sharanam,

Uyya Oraey Vazhi UdayavAr ThiruvAdi,

Alwar Thiruvadigalaey Sharanam,

Padmavathi Alarmel Mangai Thayar Samedha, Thirumalai Sri Venkatesa Perumal ki Jai,

Sarvam SriKrishnarpanam Asthu.