What words in Pali are correctly interpreted as rebirth/reincarnation?

Question

In comments to this question I saw a disagreement over the proper translation of various Pali words in suttas commonly translated with the english word rebirth or reborn.

According to Ajahn Sujato various Pali words are correctly translated as rebirth/reborn. However, another very detailed and extensive analysis by 'Element' on the linked website comes to the conclusion that none of the Pali words in the suttas are properly translated as rebirth or reborn. It appears implied that the english word 'rebirth' is synonymous with the idea of reincarnation as commonly understood by the non-Buddhist contemporary religions of India and Nepal in the time of the Buddha.

The question arises: if none of the Pali words in the suttas cited in the links above are suitably understood or translated as 'rebirth', then what Pali words in the suttas were used to describe the idea of reincarnation as commonly understood by the non-Buddhist contemporary religions of India and Nepal in the time of the Buddha?

Answer 1

One strong impression from the Pali suttas (due to the lack of discussion with Brahmins on the subject in the suttas) and the little I have read of the Vedas is the Vedas did not contain any systematic teachings on the subject of reincarnation.

The impression (from the little i have read) is the Vedas taught about two worlds, namely, this world & the other world, which i imagine was the heaven of Brahma. Otherwise, three worlds, here.

For example, I recall recently reading (somewhere) Sariputta & Moggallana were formerly disciples in a sect that believed in going to heaven with Brahma after death.

My vague recollection from chatsite banter, including by the Ven. Sujato himself, is systematic doctrines of reincarnation began forming in the later Upanishads; which 'reincarnation' aficionados, such as Sujato, who appear to go for refuge in non-Buddhist scholars, attempt to date prior to the Buddha; even though there is no account of any Upanishads in the suttas.

My recollection is the Ven. Yuttadhammo has posted on these matters, here and here.