Round World version of the Silmarillion
The Round World version is one of the variants of J.R.R. Tolkien's Legendarium, published in the final volumes of The History of Middle-earth. In this version, the setting of his legendarium is more realistic and less mythological: the Earth was always round, and Arda was the name for the whole solar system instead of just the Earth.
In the Round World version the Sun and the Moon were not the fruit of the Two Trees, but actually preceded their creation. The significance of the Trees and the Silmarils was that they preserved the light of the Sun before it was tainted by Melkor when he ravished Arien.
While this version emerged in the late stage of Tokien's legendarium, he never entirely decided which version—Flat or Round—to choose as 'real', and while Tolkien was eventually more inclined to use the realistic version, it was never as complete as the Flat World version, and so the latter was chosen by Christopher Tolkien for the published The Silmarillion.
The Round World version can be deemed by Tolkienists as the definite 'actual' story behind the text; the text of the Quenta Silmarillion then, can be seen as just the legends based on the 'reality', written by the ancient people of Middle-earth.