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.
Management (or managing) is the administration of an organization, whether it is a business, a not-for-profit organization, or government body. Management includes the activities of setting the strategy of an organization and coordinating the efforts of its employees (or of volunteers) to accomplish its objectives through the application of available resources, such as financial, natural, technological, and human resources. The term "management" may also refer to those people who manage an organization.
[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)"