The antagonisms between Russia and the "collective West" require comparation of the newly emerging international situation with that of the Cold War. The basic methodological approach in this article is, therefore, historical-comparative. Therefore, in the first part of the Paper, the phrase "new Cold War" is defined and the change in its use during the previous decades is followed, with an attempt to determine the transformation of international relations from the era of the old, classic "Cold War" to the present day. This phrase was first used during the eighties of the last century to describe the second, the final phase (1979-1985) of the original Cold War between the two superpowers of that era, which ended with a new detente, Soviet Perestroika and the Reagan-Gorbachev negotiations. Later it was used to describe the heightened contemporary political, military, social, informational and ideological tensions between the US (and its allies) on the one hand, and Russia and China on the other. Then, in the second part of the Paper, the basic characteristics of the old "Cold War" are described (the dominance of the military-strategic approach in superpower relations, proxy wars, fear of a nuclear escalation, the division of the world into spheres of interest, the primacy of ideology in the conflict between two superpowers, classic geopolitical background of ideological competition). The "New Cold War" is characterized by regional and not global competition, the disproportion in economic power of Russia in relation to the West, the absence of a deeper ideological dimension of the conflict, the dominance of the geopolitical, territorial dimensions of the competition, the existence of third powers that are uniting with Russia against the West, the integration of the conflicting parties in single world capitalist system... In the final part of the Paper, it is concluded that the differences between the old and "New Cold War" confrontations lie, first and foremost, in the structural transformation of contemporary international relations in the direction of multipolarism through a new distribution of world power that yesterday's dominant, hegemonic world power wants to prevent or at least to slow down, and we can all see the decline of the power of the West and the rise of the power of the recovered and new centers of global power in the emerging multipolar world. The US wants to use the "New Cold War" confrontation to protect its previously acquired positions, weaken its rivals and prevent them from strengthening their position and influence in contemporary international situations. These circumstances, however, do not favor the success of such action - for the simple reason that the world has changed dramatically compared to that of more than three decades ago, when the first Cold War ended. The power of the West, both economic, political-ideological and military, is constantly declining, while the power in other centers is permanently strengthening in most of these parameters. In addition, these power centers are interconnected, so it is impossible to implement the isolation measures of the old Cold War period towards them. And finally, there are the internal problems of Western societies themselves: increased social problems, lowest ever levels of trust in their own elites, increased inequality, turning of democratic elections into an empty form with predetermined outcomes, mass immigration that the West is unable to assimilate and convert to "their cultural code"... All this, unless there is a nuclear escalation, indicates that the outcome of the new Cold War will be completely different from the outcome of the first one.