Satyadvaya

Satyadvaya [alt. dvayasatya] (P. saccadvaya; T. bden pa gnyis; C. erdi 二諦) refers to two aspects of reality (satya): the relative aspect (saṃvṛtisatya ) and ultimate aspect (paramārthasatya ).

These two aspects are typically described as "two truths," "two satyas," "two realities," etc.

The Rangjung Yeshe dictionary states:

Relative truth describes the seeming, superficial and apparent mode of all things. Ultimate truth describes the real, true and unmistaken mode.^[1]

The 84000 glossary states:

Later schools of Buddhism defined and categorized the two truths in varying ways, but in all cases the presentation of the two truths is understood to be an exhaustive categorization that includes all phenomena. Note that the two truths are not understood to be separate dimensions, but rather as two aspects of the same reality, although from the perspective of the relative truth reality is falsely perceived.^[1]

Thomas Sherab Drime states:

The two satyas are conventional satya and ultimate satya. For a simple explanation: the various different manners of appearance of external phenomena, being apparently external are called conventional satya; the actual essence of these phenomena is called ultimate satya.

On a translation point: I think simply translating bden pa as "truth" is grossly oversimplifying it. Replace satya with truth, and the above sentences don't make sense anymore. If external things are a truth, a true statement, just what is that statement and what is being asserted? Here it makes much more sense to use "reality".^[2]

Treasury of Precious Qualities states:

The range of [the Buddha’s] teachings is conceivably vast, but they are all summarized in the doctrine of the two truths.

The relative truth embraces all the phenomena of samsara or the world, in other words, the mind and the phenomena that manifest from the mind. The absolute truth refers to supramundane primordial wisdom, self-knowing awareness, which has the same nature as the dharmadhatu. It follows from this that all possible knowledge-objects are accounted for in the two truths; there is no third truth.

[...]

The two truths are not separate like the two horns on a buffalo. From the beginning they are inextricably blended together: appearance and emptiness inseparably united. Therefore, phenomena arising through interdependence are not totally nonexistent like a horned rabbit. They are rather like the reflection of the moon in a clear pool. Phenomena appear, and this aspect of appearance corresponds to the relative truth. Nevertheless, in the very moment of their arising, they are lacking in true existence. This aspect corresponds to the absolute truth. Thus, while a distinction can be made between the two truths, these same two truths have no intrinsic existence separate from each other.^[3]