Yes, Tirupati Balaji is the same as Lord Krishna. In the Srinivasa Kalyana of the Bhavishyottara Purana, there is a story. When Srinivasa was living with Bakula Devi, at that time, one day He planned to go hunting. He remembered Vayudeva, who came in the form of a horse. He sat on the horse. He was nicely decorated with Urdhva Pundra, peetambara, and all. He was coming to the forest when He saw a group of girls playing. These girls were none other than Padmavati Devi and Her sakhis, who were playing with a ball.
Sage Narada came and met Padmavati Devi. He saw Her lips, which were red like a pomegranate, Her teeth, which sparkled like pearls. Her eyes were large and like a bloomed lotus; Her face resembled that of a spotless Chandra. On seeing Padmavati Devi, who was none other than Lakshmidevi Herself, who was born to Aakasha Raja, Sage Narada bowed down to Her in His mind. He said, “You are so fortunate that Lakshmipati Narayana would Himself be your husband.” Padmavati Devi, in order to teach how one should respect elders, bowed down to Sage Narada, and Sage Narada blessed Her outside, but from inside bowed to Her, and went away.
Here, while Srinivasa was hunting animals like lions, deer, sharabha, etc., He saw a male elephant and chased it. That elephant ran and came near the area where Padmavati and Her sakhis were playing. On seeing the elephant, they were all frightened and closed their eyes. The elephant bowed to Srinivasa by lifting its trunk and disappeared. All of them saw this handsome man sitting on the horse, looking like Manmatha, but in reality He was the father of Manmatha. Padmavati Devi asked Srinivasa as to who was He. At this, Srinivasa said, “I am from Chandra Vamsha, and gotra – Vasista Gotra. My father is Vasudeva, mother Devaki, Balarama is my brother, Subadra is my younger Sister, Arjuna is my friend, and all Pandu putraas are my relations. I am the eighth son of Devaki. The seventh son of my parents is Balarama. As I was born in Krishna Paksha and I was Krishna varna (black colour) like my mother, I was called Krishna.”
This incident itself proves that Srinivasa or Tirupati Balaji is Krishna Himself, who is Srimannarayana. There is no difference between Srinivasa and Krishna. During Srinivasa Kalyana Mahotsava too, it is said:
“Grandson of King Shoorasena, Son of Vasudeva, SriKrishna…”
Similarly, Padmavati Devi is also from Chandravamsha only. In Dvapara Yuga, when Yashoda met Krishna, after Krishna left Vrindavana, she says, “I saw your Baalaleelas, but couldn’t see any of your marriages with Rukmini, Satyabhama, etc.” At this, Krishna smiled and said, “O Mother! Don’t worry. In the 28th Kaliyuga, I will appear on earth as Srinivasa, and you will be born as Bakula Devi. In that birth, you will see my Kalyana with Padmavati Devi, who will be Lakshmi/Rukmini Herself.”
So, as per that boon of Krishna, this Yashoda was born as Bakula Devi, who used to serve Lord Bhuvaraha in Sheshachala Parvata. Srinivasa, who was Krishna in the earlier avatar, came to her, stayed with her, and showed her His divine marriage with Padmavati Devi. So, Srinivasa is Krishna Himself, and there is no difference between the two in mood, qualities, valour, strength, knowledge, beauty, opulence, etc.
Srinivasa, after His marriage with Padmavati is decided, calls all His family members. Brahma was His son. Lord Shiva is His grandson, and other devatas and all were His family members. Then Srinivasa felt the absence of Lakshmidevi. Lakshmidevi was in Karaveerapura. So, He asked Suryadeva to go and tell Lakshmidevi that Srinivasa is so ill that He cannot even take a step and is suffering from utter weakness. Surya went to Karaveerapura and informed Lakshmidevi. Lakshmidevi, though, knew that Srinivasa is devoid of all flaws like weakness and all, came on Garuda to Sheshachala Parvata, as if She was too worried about Srinivasa, acting as per His will. Lakshmidevi saw that Srinivasa was resting by keeping His head on Brahma’s thigh and legs on Shiva’s thigh. Srinivasa said, “L-La-Laks-Lakshmi…”
Lakshmidevi laughed and requested Him to stop His naataka and then did Tailabhyanjana snaana to Him. Tailaabhyanjana means ‘oil bath’. So, at that time She says:
धीर्घायुर्भव गोविंद बहुपुत्रो धनाधिप: ।
चतुर्दशनानां लोकानामेकछत्रादिपो भव ।
Here, She calls Srinivasa Govinda, which is a popular name of Krishna as well as Srinivasa. Govinda means Krishna only. So, this also proves that Krishna is Srinivasa and Srinivasa is Krishna. Dheergaayurbhava Govinda – Lakshmidevi said this only for loka shishanartham. You are the owner of the entire world. You are the Ekachatradhipathi for all the 14 lokaas. By saying so, She applied oil for the aprakurtha deha of Srinivasa and gave him an oil bath as abhisheka for Srinivasa.
[Srinivasa of Tirupati]
Hope this helps!
Jay SriRam!
SriLakshmiPadmavati Sameta SriSrinivasa Abhinna SriKrishnarpanamastu!