Well to start with, the vikings and varangians were the same group of people. The men, and I do mean men the evidence for women who bore arms in norse society is complicated, who left Scandinavia to make their fortunes abroad either around the North Sea, or the Mediterranean/Black Sea, were doing so for similar reasons, and this reason was fundamentally economic in nature.

The Norse people, either in England, Ireland, Byzantium, Russia, or anywhere else were not there by accident. These people were venturing out in the expectation of receiving some form of monetary benefit for it. This is partly why it is so difficult to firmly classify individuals as vikings or as traders or merchants. In all likelihood the members of expeditions that raided in England, traded in Russia, and served as mercenary forces in Byzantium were all operating in a similar fashion. The point of viking raids was not to sow wanton destruction, but to acquire wealth. Ideally wealth that could be moved around and exchanged easily. This is why the Norse came to dominate trade systems such as the exchange of lumber, furs, and slaves across the North Sea world and connected parts of North America to the Islamic caliphates in modern day Iraq into one hemisphere spanning trade network.

These people were largely of the same economic, and social, class as well. In viking age Scandinavia it was the warrior elites of society who provided the bulk of men and materiel of overseas expeditions. Men who had significant status as lords needed to provide gifts and other privileges to their followers and these overseas raids were one method by which goods and power could be obtained and distributed, however trade relations could often accomplish similar goals. Remember, the end goal of the raids and trade and so on were all the same, economic and social advancement, it was the methods that different groups adopted that separated them, not their motives. These are the "push" and "pull" factors that you mention in the OP. Social and economic advancement were the goal, raids, trading, and colonization efforts were the means by which that goal was achieved. Indeed, these same push and pull factors were actually somewhat unchanged for centuries, and there is an argument to be made that the Scandinavia migrations, raids, and so one were a continuity of the similar movements that characterized the end of the Roman Empire in Western Europe. It was the lure of Roman wealth that lured many Germanic and other groups of people to enter the Empire, and even after its collapse in the west, similar motives were still at play, the frontier had just shifted as the western European economy shifted from being more Mediterranean based to a riparian system with the North Sea as the major site of exchange.

As for the cultural differences between Eastern and Western Europe.... No. The Scandinavian influence on these areas is not responsible for the totality of differences between these parts of the world, but fully answering why Eastern and Western Europe are different is the kind of project that you could fill thousands of pages in multiple books in and still not arrive at a firm conclusion.