How Divisions of Eastern Slavs Came to Be

 Two biggest and oldest cities were Kyiv in modern Ukraine and (Great) Novgorod. Then other cities were founded in different directions. Halich, Chernigov, Rostov, two Volodymirs one in northwest Ukraine and other in east of Moscow in Russia. 

These cities were under their own rulers and for the most part independent from each other, there was a rotation rulership system for some time but then they just settled for near complete independence. Only religion was somewhat unified with one Patriarch of Kyiv. Yuri Dolgoruky convinced him to relocate to Vladimir (East one) and then to Moscow. From that Moscowy later claimed the right to rule over the whole former Rus.

However real division emerged from when Lithuanians conquered or unified the Western principalities. and Golden Horde eastern ones. What fell into Golden Horde sphere ended up modern Russia. What ended up in Lithuania, Belarus and Ukraine.

Further division between modern Belarus and Ukraine emerged when last Jagellon, transferred southern Voivodships from Lithuania to Poland. It was part of internal reorganization and transformation within Poland-Lithuanian Union, that was becoming more structured and organized. Rzeczpospolita, was then divided into two main subdivisions: Poland (Corona), that consisted of parts of modern Poland and West and Central Ukraine and Lithuania (Litva), modern Lithuania and Belarus. Before that reorganizations, Central Ukraine and Vohlynia, was part of Lithuania as well. However, Galicia was part of Poland even before that reorganization. Galicia was actually the first area to call itself Kingdom of Rus, before it was incorporated into Poland. Many centuries before Muscovy laid such claims.

In the east Golden Horde extorted tribute money from Rurikids princes, threatening to burn down their cities if they do not pay the Horde off. Protection racket as a form of government.

Three main branches of Rurikids were affected by that: Rostov (lake Nero)-Suzdal-Vladimir-Muscovy Principality (modern Golden Ring were their core lands), eventually emerged as dominant there. They eventually became Muscovy.

Tver and Ryazan principalities also suffered Golden Horde protection racket. Later their lands were conquered and incorporated into Muscovy. Tver did separated from early version of Muscovy, but often fought against Muscovites. Ryazan used to be part of modern-day Ukraine Chernigov Principality instead.

Novgorod was not part of Golden Horde, but rather Hanseatic league system. However, Muscovy conquered them shortly before Tver and Ryazan.

Eventually Rzeczpospolita consolidated in the West, Muscovy emerged from collapse of the Golden Horde in the East. Cities like Smolensk became their border areas and were constantly fought over, changing hands regularly. 

Fundamentally the West areas (Ukraine, Belarus) managed to retain most of the original character of the Rus. Rzeczpospolita was fundamentally western state. Rurikids came from modern day Sweden, Denmark or Baltic areas.

Russia on the other hand was exposed to a lot of Eastern Persian and Chinese influences through the Golden Horde system. Eventually Muscovy conquered and incorporated Tatar's Khanates of Kazan and Astrakhan, further making Russia some hybrid/fusion East-West entity. Turkic, Slavic, Finnic, Scandinavian and East Asian people are mixed into a single identity.