Could you clarify your question further? For example, are you referring to English usages? Belarus means White Russia, and it is literally called White Russia in some languages.
Little Russia
In the High Middle Ages, a powerful Slavic state arose in modern-day Ukraine, Belarus, and western Russia. Because the people called themselves the Rus’ and their capital was situated in Kiev, this state came to be known as the Kievan Rus’. Many of the Slavs of the areas under their authority were initially pagans. By the 13th Century, however, many of the Slavic tribes had converted to Orthodox Christianity. After the Mongols destroyed Kiev in the mid-13th Century, two rival successor-states—Galicia-Volhynia and Suzdalia—and many other states arose in its place.^(1)
The Orthodox Church under the Kievan Rus’ answered to its leader, the metropolitan bishop. The metropolitan bishop—or the metropolitan for short—was known by this title because he was the supreme clerical authority of the metropolis of Kiev. With Kiev destroyed, however, the metropolitan had to move his headquarters elsewhere. He decided to move to Suzdalia. His decision to move to Suzdalia symbolically granted that country an air of legitimacy as the true successor state to the Kievan Rus’. The leaders of Galicia-Volhynia were well aware of the prestige this granted Suzdalia, and therefore insisted that the metropolitan move his headquarters to their country instead. Wishing to avert further conflict, the metropolitan stayed in Suzdalia, but granted Galicia-Volhynia its own metropolitan.^(2)
In order to distinguish between the two metropolitans, the clerical authorities began referring to Suzdalia as “Major Rus’”, and to Galicia-Volhynia as “Minor Rus’”. At the time, the use of “major” and “minor” may have only indicated that Galicia-Volhynia had fewer eparchies, or clerical provinces. By the 1330s, even secular rulers started referring to the two countries by these terms.^(3)
After the Polish conquest of Galicia-Volhynia, the terms “Major Rus’” and “Minor Rus’” fell into disuse. By the 17th Century, the leaders of Muscovy began styling themselves as the leaders of not just Muscovy, but “Russia”, the Greek variant of “Rus’”. With the introduction of the term “Russia”, the terms “Major Rus’” and “Minor Rus’” were revived as “Great Russia” and “Little Russia”. Muscovy was understood to be “Great Russia”, and the majority-Orthodox Christian territories of modern-day Ukraine comprised “Little Russia”.^(4)
Ukraine at the time was known by many, many terms. “Ukraine” and “Little Russia” were only two of those terms. In the mid-17th Century, the Tsar of Muscovy—now “Great Russia”—officially changed his title to “Tsar of Great and Little Russia”. With official recognition, the term “Little Russia” became the generally accepted term for Ukraine by the 18th Century.^(5)
In the last century, growing nationalism in modern-day Ukraine led to a widespread preference for “Ukraine” over “Little Russia”. The term “Little Russia” implied that the people of Ukraine were only one branch of a larger Russian ethnicity, an idea that ran counter to the nationalist sentiment that had enveloped the country. As a completely different term, “Ukraine” implied an ethnic distinction between Russians and the people of Ukraine.^(6)
White Russia
Nobody is entirely sure how modern-day Belarus came to be known as “White Russia”. Some believe that the name originated from the white clothing that the people in that region wore.^(7) Others believe it originated from the heavy snowfall the region seasonally experiences.^(8) Another possible theory is that the names of many places situated in eastern-central Europe—the old towns of Belsk, Białystok, Beloveža, and Bela, and the rivers Belaja and Beljanka—all closely resembled the root word for “white” common to virtually all Slavic languages. From these names, the whole region came to characterized as a “white” region.^(9) Another theory claims that the term originated from a Byzantine emperor who used the term “white” to distinguish Christian Slavs from pagan ones.^(10) Yet another theory claims that the Russian word for “white” derives from the pagan Slavic deity Belbog, whom the ancient Slavs of modern-day Belarus and Ukraine worshipped. Because these people worshipped a “white” god, they came to be known as a “white” people.^(11)
Another theory claims that the people who inhabited modern-day Belarus were actually Balts and not Slavs. There is a phonetic similarity between “Belbog” and “Bäldäg”, a Baltic-Teutonic god whose name—according to this theory—means “white day”. Given the phonetic similarity between the Slavic root word for “white” and the words “Belbog”, “Bäldäg”, and “Baltic”, supporters of this theory contend that the supposed “Balts” who inhabited what is now Belarus perceived themselves as a “white” people.^(12)
Yet another theory claims that the words “běla,” and “běl’” were used to denote white-colored currency that was used in the region.^(13)
A final theory traces the word “white” to how the Tartars used the word. “White” denoted the ruling Tartar clans, and “black” denoted their vassals. The Slavs—whom the Tartars conquered and vassalized—adopted this particular way of using the words “white” and “black”. “White houses”, “white cities” and “white outposts” were therefore founded as places connected to the ruler of a region who granted these locales special privileges. Often, these privileges entailed exemption from tribute and taxation. This also applied to Church estates, which were known as “white lands”. Lands and people which were not exempt from taxation—and so were in some sense “enslaved” to a ruler—were denoted as “black”. The color white eventually came to be associated with a very specific notion of freedom often connected to leadership.^(14)
So the theory goes that the Poles gave the appellation “white” to the Western Slavic lands that the Lithuanians “rescued” from Muscovy. Taking these lands from Muscovy—then a vassal of the Tartars—meant that the principalities situated in these lands were now themselves no longer vassals of the Tartars. They were now liberated from the Tartars, and therefore “white”. Hence the name “White” Russia.^(15)
Unlike “Little Russia”, the term “White Russia” technically never went out of use. The name of the modern country of Belarus quite literally means “White Russia”.
Endnotes
1 Kohut, Zenon E. “The Development of a Little Russian Identity and Ukrainian Nationbuilding.” Harvard Ukrainian Studies, vol. 10, no. 3/4, 1986, pp. 559–576, p. 562
2 Ibid. p. 563
3 Ibid.
4 Ibid. p. 563-4
5 Ibid. p. 565
6 Plokhy, Serhii. “Ukraine or Little Russia? Revisiting an Early Nineteenth-Century Debate.” Canadian Slavonic Papers / Revue Canadienne Des Slavistes, vol. 48, no. 3/4, 2006, pp. 335–353, p. 340
7 Vakar, Nicholas P. “The Name ‘White Russia.’” American Slavic and East European Review, vol. 8, no. 3, 1949, pp. 201–213, p. 201
8 Ibid.
9 Ibid. p. 203
10 Ibid. p. 204
11 Ibid.
12 Ibid. p. 205
13 Ibid.
14 Ibid. pp. 206-9
15 Ibid. p. 209
Sources
Kohut, Zenon E. “The Development of a Little Russian Identity and Ukrainian Nationbuilding.” Harvard Ukrainian Studies, vol. 10, no. 3/4, 1986, pp. 559–576.
Plokhy, Serhii. “Ukraine or Little Russia? Revisiting an Early Nineteenth-Century Debate.” Canadian Slavonic Papers / Revue Canadienne Des Slavistes, vol. 48, no. 3/4, 2006, pp. 335–353.
Vakar, Nicholas P. “The Name ‘White Russia.’” American Slavic and East European Review, vol. 8, no. 3, 1949, pp. 201–213.
Edit: Formatting, wording
Color terms and size terms for the different Russias have different origins.
A Rus of Colour first starts appearing as the Latin Calque, "Ruthenia rubra" or "Russia rubra", of "Czerwień Rus", of a region which has originally been called after the city of Czerwień. The city, however, was destroyed by the Mongols in the thirteenth century and thus the region bearing it's name (today it's the West of Ukraine) was reinterpreted to be derived from the Slavic word for "red". Later maps would also include a White Russia and a Black Russia to cover the parts of christian orthodox Eastern Europe which weren't "red" (and those terms could wander anywhere from Lithuania to Moscow and from the White to the Black Sea).
"Great Russia" was picked up from the Byzantines (drawing, in turn, from classical conventions).
White Russia remained the term used for Belarus (it is the meaning of Belarus) while the Little/Great division was dropped because it was considered demeaning by Ukrainian nationalists (who preferred the term Ukrainian) as well as the Bolsheviks (Lenin having attacked "Great Russian Chauvinism").
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