What does Nonduality correspond to in Buddhism?
There's an article on that subject Dhamma and Non-duality by
Bhikkhu Bodhi.

The following is basically all direct quotes from that article, except very summarized (I'm extracting sentences and sentence fragments).



Non-dual system

For the Vedanta, non-duality (advaita) means the absence of an ultimate distinction between the Atman, the innermost self, and Brahman, the divine reality, the underlying ground of the world.

The Mahayana schools, despite their great differences, concur in upholding a thesis that, from the Theravada point of view, borders on the outrageous. This is the claim that there is no ultimate difference between samsara and Nirvana, defilement and purity, ignorance and enlightenment. For the Mahayana, the enlightenment which the Buddhist path is designed to awaken consists precisely in the realization of this non-dualistic perspective. 

Not a non-dual system

As for the Theravada tradition:


Virtue


Non-duality: the adept isn't bound by rules because "The sage has transcended all conventional distinctions of good and evil"
Theravada: "the liberated one lives restrained by the rules of the Vinaya, seeing danger in the slightest faults"

Meditation:


Non-duality: defilements are mere appearances devoid of intrinsic reality
Theravada: hindrances are "causes of blindness, causes of ignorance, destructive to wisdom, not conducive to Nibbana"

Wisdom:


Non-duality: concrete phenomena, in their distinctions and their plurality, are mere appearance, while true reality is the One: either a substantial Absolute (the Atman, Brahman, the Godhead, etc.), or a metaphysical zero (Sunyata, the Void Nature of Mind, etc.). For such systems, liberation comes with the arrival at the fundamental unity in which opposites merge and distinctions evaporate like dew
Theravada: wisdom not in the direction of an all-embracing identification with the All, but toward disengagement and detachment, release from the All





So to answer your question, if I understand the article, it's saying that "non-duality" in Buddhism includes statements like "nirvana and samsara are the same" and "everything is equally empty" ... but non-duality is not a feature of Theravada Buddhism (it's a feature of Mahayana Buddhism, and of Tantrayana).