die Führung
leadership
The direction and management of a group, company, or organization.
Unter seiner Führung hat das Unternehmen große Erfolge erzielt.
Under his leadership, the company achieved great success.

leadership / tour / lead
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leadership
The direction and management of a group, company, or organization.
Unter seiner Führung hat das Unternehmen große Erfolge erzielt.
Under his leadership, the company achieved great success.

The noun 'die Führung' is derived directly from the verb 'führen' (to lead). This connection helps you recognize the basic meaning of leading or guiding in all uses of the word.
Ein guter Kapitän führt seine Mannschaft sicher durch den Sturm.
A good captain leads his crew safely through the storm.
The context reveals the meaning: in connection with a company, it is about management. In a museum or a city, it means a guided tour. In sports or a race, it refers to first position.
Die neue Führung des Konzerns stellte ihre Pläne vor.
The new leadership of the corporation presented its plans.
In a management context, the preposition 'unter' (under) is often used. Typical phrases are 'die Führung übernehmen' (to take over leadership) and 'unter der Führung von jemandem stehen' (to be under someone's leadership).
Unter der neuen Führung wurden viele Prozesse modernisiert.
Under the new leadership, many processes were modernized.
When referring to a tour, the most common verbs are 'eine Führung machen' (to take a guided tour), 'an einer Führung teilnehmen' (to participate in a guided tour), or 'eine Führung anbieten' (to offer a guided tour).
Möchtest du an einer Führung durch das Kunstmuseum teilnehmen?
Would you like to take part in a guided tour of the art museum?
In sports contexts, the phrases 'in Führung gehen' (to take the lead) or 'in Führung liegen' (to be in the lead) are often used. Other typical verbs are 'die Führung ausbauen' (to extend the lead) or 'die Führung verlieren' (to lose the lead).
Die Heimmannschaft ging schon nach zehn Minuten in Führung.
The home team took the lead after just ten minutes.
The meaning as a technical component is typical of specialized language in trades and technology. In everyday life, you will hear this meaning less often, unless you are repairing something.
Der Monteur musste die Führung der Rollläden austauschen.
The technician had to replace the guide rail of the shutters.
government
'die Regierung' and 'die Führung' can both have to do with leading and making decisions. However, 'die Regierung' specifically means the political leadership of a state or country. 'die Führung' is more general and also fits companies, clubs, teams, or organizations. In political texts, 'Führung' can sometimes sound similar, but it is less precise than 'Regierung' when you really mean the official group at the head of the state.

Die Führung der Firma erklärt den Mitarbeitern die neuen Pläne.
The company's leadership explains the new plans to the employees.
Wegen der Krise berät die Regierung heute über neue Hilfen.
Because of the crisis, the government is discussing new aid measures today.