Hindu scripture describes two Buddha Avataras of Vishnu born to deceive people. One Buddha Avatara took place during the Tripura incident. Another Buddha Avatara took place in the present Kali Yuga. Some people identify this second Buddha Avatara with Siddhartha Gautama, the founder of Buddhism who is commonly called Buddha. Others think they’re two different people, and that Siddhartha Gautama was not an Avatara of Vishnu.
My question is, what is the earliest reference to Siddhartha Gautama either being the same as Vishnu’s Buddha Avatara or the two being different. What are the earliest work of Acharyas that discuss this issue?
Note that I’m not looking for answers which try to argue the substance of whether the scriptural descriptions of the Buddha Avatar matches what we know about Siddhartha Gautama. I’m just looking for the earliest explicit reference to this issue of whether they’re the same or not.