TMingyur wrote:What strikes me in this thread is that it is implied that "buddha nature" is unanimously accepted in all schools of Mahayana and that if the term as such is accepted then there would be one meaning that is unanimously implied by all schools of Mahayana.
This is definitely not so. E.g. Madhyamaka does not hold the Tathāgatagarbha view and some schools of Madhyamaka explicitely reject all interpretations of "buddha nature" that imply something other than a mere non-affirming negation (i.e. emptiness).
Your key point here, if I understand, is not that the Madhyamaka (and others) reject "buddha nature", but reject a particular interpretation of "buddha nature".
Greetings Without Colour,
To the best of my knowledge, neither of these terms (nor what they point to) are recognised in Theravada.
Paul's attempt at rejecting "buddha nature" in terms of a "buddha element" are only applicable to the affirming position vis this doctrine, but not with regards the Madhyamaka position. Simply reading the words "buddha-dhatu" and thinking that we now understand what all Mahayana schools mean by this is misrepresenting those schools. How can we then come to an understanding or answer the original question? Paul after all does state "what they point to", but unfortunately has not made the investigation to find out what they actually do refer to, and apparently doesn't even think that it is appropriate int his thread to find out!
Many Mahayana schools understand "tathagatagarbha" and "buddhadhatu" as synonyms for emptiness. This is almost always a strictly non-reified position, and in many cases extremely similar to Theravada positions on emptiness as not self. In fact, I may even go so far as to suggest that a majority of Indo-Tibetan schools read it in this way, and a fair portion of the east asian schools, too.
Thus, in this sense at least, although they may not use those exact words "tathagatagarbha" and / or "buddhadhatu", doctrinally there is a fair amount of commonality. As the second reliance states: Rely on the meaning, not on the words.