Two interpretations of the three levels of suffering, Dukkha Sutta and Tibetan There's a wrinkle in the teachings about the three levels of suffering. The Pali Canon, in SN 38.14 -- Dukkha Sutta -- has it thus (leaving things uninterpreted for the moment):


the suffering of pain (dukkha-dukkhatā)
the suffering of fabrication (sankhāra-dukkhatā)
the suffering of change (vipariṇāma-dukkhatā)


The Tibetan teachings typically have it in the following order (Gampopa, Jewel Ornament of Liberation, Chapter 5, has the reverse):


the suffering of suffering -- overt, obviously painful stuff.
the suffering of change -- suffering implicit in pleasure because of impermanence, so it will end
all-pervasive suffering -- suffering due to conditioned existence itself, and the aggregates which are of the nature of suffering


The Tibetan teaching is widely interpreted as I have indicated (though a lot of the descriptions of all-pervasive suffering shade into the definition of suffering of change, which they shouldn't IMHO).

A lot of commentators (such as Guenther on Gampopa) see SN 38.14 as the source of the the Tibetan teaching, and the first items of each do seem to line up nicely, as do the suffering of change in both. But after that there are problems, mainly, why did the order change. 

Most pervasively, there is an interpretation (by contemporary teacher Bodhipaksa) of SN 38.14 where the two sufferings of change don't even totally line up, and maybe the whole correspondence is wrong and is more about the two-arrow teaching of SN 36.6 -- The Sallatha Sutta -- than levels of suffering, and referred to in this SE answer: that correct interpretation of SN 38.14 is roughly:


the suffering of pain (dukkha-dukkhatā) -- the initial pain -- the "first arrow"
the suffering of fabrication (sankhāra-dukkhatā) -- the constructed pain we add by resisting/resenting/etc the initial pain -- the "second arrow"
the suffering of change (vipariṇāma-dukkhatā) -- the suffering we get by seeking to cover the constructed pain with pleasure, which is impermanent.


The change in order, putting suffering of formations/conditioned existence in the middle, is the smoking gun, according to Bodhipaksa -- if the Tibetan interpretation of SN 38.14 were correct, then suffering of formations would absolutely have to come last.

So finally my question -- not which is "correct" but -- when did the Tibetan interpretation arise, if not an entirely new teaching, at least the change of order and interpretation of suffering of formations as universal, all-pervasive suffering rather than a personal, second-arrow kind of deal. Is is it in the Theravada anywhere?

The farthest back I can find it is Gampopa, whose Jewel Ornament of Liberation is (I believe) the first fully articulated, book-length Lam Rim text, after Atisha's Lamp for the Path to Enlightenment which is the origin of the Lam Rim, but only has 68 verses and does not go to this level of detail. Seems that those are close enough to the beginning of Buddhadharma in Tibet that the next stop back, if there is one, is probably India or maybe a Nyingma teaching.

Addendum -- Toni Bernhard, Author of How to be Sick and other books, explicates the non-Tibetan, Bodhipaksa version of three sufferings.

Addendum -- There is another sutta with the same sequence as SN 38.14, namely SN 45.165 -- The Dukkhata Sutta. Well known contemporary scholar, translator and practitioner Maurice Walshe has this translation and interpretation of SN 45.165 that accords with the Tibetan reading, despite the sequence.
The words in SN 38.14 are not even attributed to Buddha, they are Sariputra's. I don't know why Theravada took them as the basis of their analysis.

Instead, the authoritative definition of dukkha is found in SN 56.11, the first and main sutra of Buddhism, The Sutra of Setting the Wheel of Dharma in Motion:


  Now this, wanderers, is the nobles' truth of dukkha: Birth is dukkha, aging is dukkha, death is dukkha; sorrow, lamentation, pain, grief, and despair are dukkha; association with the unloved is dukkha; separation from the loved is dukkha; unsatisfied thirst is dukkha. In short, the five heaps of fuel (upadana-skandha) are dukkha.


As I understand, in Tibetan classification "the suffering of suffering" is a generalization of the apparent dukkha such as the pains of "birth, aging, death, sorrow, lamentation, pain, grief, and despair". "The suffering of change" is a generalization of "association with the unloved / separation from the loved" aka "the unsatisfied thirst", and "the all-pervasive suffering" stands for the "In short, the five heaps of fuel are dukkha". The sequence preserves the ordering of the original Buddha's quote.