Two interpretations of the three levels of suffering, Dukkha Sutta and Tibetan
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.