There’s something paradoxical or even ironic about the concept of the conventional (saṃvṛti) being understood as a kind of “truth” (satya), since in some interpretations of the two truths the conventional is understood as false in contrast to the ultimate (paramārtha) which is alone true. Generally, according to these views, often associated with the Sakya school through figures like Gorampa Sonam Senge, you can distinguish between true and false within the terms immanent to the domain of conventional truth, but must also recognize that all conventional truths are categorically false in terms of the domain of ultimate truth. In this view the two truths are radically distinct considered on their own yet understood to be equal from the ultimate standpoint. Because the ultimate negates the conventional, there is something “positive” to the ultimate even if it cannot be characterized explicitly.
Tsongkhapa Lobzang Drakpa is a notable exception to this because he believes that there are genuinely two truths and not just the one ultimate truth that subsumes the conventional. He thinks that conventional truth is not only genuine truth, but that the ultimate truth itself is a conventional truth. His view is often associated with the Gelug presentation of the two truths as “conceptually distinct but essentially identical.” Because the ultimate is reduced to the conventional, the ultimate is characterized as a complete absence with no positive content i.e. the “lack of inherent existence.”
You may characterize the view in which the ultimate truth includes and subsumes the conventional truth as being eternalistic about the ultimate and nihilistic about the conventional; likewise, you can characterize Tsongkhapa’s view in which ultimate and conventional truth exist simultaneously as indivisible aspects of the same thing as being eternalistic about the conventional and nihilistic about the ultimate.
I tend to gravitate towards Jamgön Ju Mipham Gyatso’s take on the two truths, which is like a kind of dialectical synthesis of the other two approaches: For Mipham the Gelug-style view in which the ultimate is a mere absence is understood to be a “true” characterization of the ultimate yet one contained in the domain of explicability. There is another “truth” that lies beyond the domain of explicability, the domain of ultimate truth that is characterized as “freedom from extremes” or “freedom from conceptual proliferation.”
The relationship between the truth beyond explicability and the truth within explicability is like that of the relationship between the moon and its reflection on a mirror: the reflection of the moon accurately depicts some of the character of the moon, but is not actually the source of the reflection itself, which lies beyond the surface of the reflection. Nonetheless it would be inaccurate to say that the reflection of the moon bears no characteristics of the actual moon. Similarly, the explicable ultimate truth of “emptiness” as a mere negation with no positive content is in accordance with the non-explicable ultimate that is free of extremes including the extremes of emptiness and non-emptiness.
So for Mipham the two truths are neither identical nor distinct but rather are seen to “coalesce” at the consummation of holy practice. By making use of this understanding of the final coalescence of the two truths in advance of the consummation of our own path, we can accelerate our movement to that very end. In a sense, the only real distinction between all these different views of the relationship between the two truths is based on the degree to which they help us on our path. So the “truth” of these views are not based in their correspondence to some objective reality, but rather in their ability to afford us the assistance to come into accordance with the way things are as such (tathātā).