International mostly means something (a company, language, or organization) involving more than a single country. The term international as a word means involvement of, interaction between or encompassing more than one nation, or generally beyond national boundaries. For example, international law, which is applied by more than one country and usually everywhere on Earth, and international language which is a language spoken by residents of more than one country.
International Relations (IR) or International Affairs (IA) - commonly also referred to as International Studies (IS) or Global Studies (GS) - is the study of interconnectedness of politics, economics and law on a global level. Depending on the academic institution, it is either a field of political science, an interdisciplinary academic field similar to global studies, or an entirely independent academic discipline in which students take a variety of internationally focused courses in social science and humanities disciplines. In all cases, the field studies relationships between political entities (polities) such as sovereign states, inter-governmental organizations (IGOs), international non-governmental organizations (INGOs), other non-governmental organizations (NGOs), and multinational corporations (MNCs), and the wider world-systems produced by this interaction. International relations is an academic and a public policy field, and so can be positive and normative, because it analyses and formulates the foreign policy of a given state.
It is also a fact that America is too democratic at home to be autocratic abroad. This limits the use of America's power, especially its capacity for military intimidation. Never before has a populist democracy attained international supremacy. But the pursuit of power is not a goal that commands popular passion, except in conditions of a sudden threat or challenge to the public's sense of domestic well-being. The economic self-denial (that is, defense spending) and the human sacrifice (casualties, even among professional soldiers) required in the effort are uncongenial to democratic instincts. Democracy is inimical to imperial mobilization.
Zbigniew Brzezinski,The Grand Chessboard (1997).
We must distinguish between military and political power. Political power is a psychological relation between those who exercise it and those over whom it is exercised. It gives the former control over certain actions of the latter through the influence which the former exert over the latter's minds. That influence may be exerted through orders, threats, persuasion, or a combination of any of these.
Hans Morgenthau, Politics Among Nations (1948).