Rangtong (Tib. རང་སྟོང་, Wyl. rang stong) literally means 'empty of self'. The followers of the Rangtong Madhyamika approach say that all phenomena, including the buddha nature, are empty of their own essence. They therefore disagree with the Shentong approach, which, they say, falls into the extreme of eternalism.
The self-empty and other-empty terms arose only with the new translations schools in Tibet, and are therefore not part of traditional Nyingma vocabulary. Yet this does not mean that Nyingma scholars have not been engaged in debates surrounding these issues. There are no straightforward equivalents known in Sanskrit sources, yet scholars suspect that many aspects of this debate arose with scholars as Ratnakarashanti.
As for the Nyingmapas, Mipham Rinpoche explains in the first chapter of the Beacon of Certainty that the Nyingma view falls neither in the extreme of self-emptiness nor other-emptiness. If pressed, Mipham continous, the view should be explained according to a nonimplicative negation.
From the Shentong perspective, the Rangtong view falls into the extreme of nihilism. The Shentongpas say that underlying everything there must be the uncompounded luminosity of the buddha nature, as the basis for samsara and nirvana and all the qualities of enlightenment.