Business is the activity of making one's living or making money by producing or buying and selling goods or services. Simply put, it is "any activity or enterprise entered into for profit. It does not mean it is a company, a corporation, partnership, or have any such formal organization, but it can range from a street peddler to General Motors." The term is also often used colloquially (but not by lawyers or public officials) to refer to a company, but this article will not deal with that sense of the word.
Business administration is management of a business. It includes all aspects of overseeing and supervising business operations and related field which include Accounting, Finance and Marketing.
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 business consists of trades and transactions at a global level. These include the trade of goods, services, technology, capital and/or knowledge.
[A Jew] should make Torah his principal occupation and his work his casual one. He should minimize his business pursuits and occupy himself with Torah. And he should remove fleeting pleasures from his heart, and work each day enough to maintain himself. ... The rest of the day and night, he should occupy himself with Torah.
Rema, Shulchan Arukh, Yoreh De'a, 246:21, in "Separation from the Worldly (Perishut)"
To those who run businesses, profits are obviously desirable and losses deplorable. But economics is not business administration. From the standpoint of the economy as a whole, and from the standpoint of the central concern of economics — the allocation of scarce resources which have alternative uses — profits and losses play equally important roles in maintaining and advancing the standards of living of the population as a whole.
Thomas Sowell, Basic Economics (4th ed., 2010)
An artisan busies himself with his work for three hours each day and spends nine hours in study.
Maimonides, Treatise 3: “The Study of the Torah,” Chapter 1, Section 12, H. Russell, trans. (1983), p. 52