Learn Russian: Директор управляет коллективом, а менеджер руководит отделом. - The director manages the team, and the manager leads the department.

They are in the Instrumental case. The verbs управлять (to manage) and руководить (to lead) are special verbs that require their object to be in the Instrumental case, instead of the usual Accusative case. Since коллектив and отдел are masculine nouns ending in a consonant, they take the -ом ending.

What is the exact difference between управлять and руководить?

Both mean to manage or direct, but they have slightly different flavors. Управлять often implies managing systems, processes, or operating machinery (like steering a car or running an entire organization). Руководить literally comes from the words for hand (рука) and to lead (водить), so it focuses more on personally guiding, supervising, or being the boss of a group of people.

Why use коллективом instead of командой for team?

While команда translates directly to team and is frequently used in sports or specific task forces, коллектив is a very standard Russian word for a group of colleagues or staff working together day-to-day in an office or organization.

Why does the sentence use the conjunction а for and, rather than и?

The conjunction а is used to show a slight contrast or to compare two different subjects doing different things. Here, it contrasts the director's specific responsibilities with the manager's specific responsibilities. It works a lot like whereas or while in English.