
das Unternehmen
company
An economic organization that produces goods or offers services; a company or business.
Sie leitet ein mittelständisches Unternehmen mit 50 Mitarbeitern.
She runs a medium-sized company with 50 employees.
company / undertaking
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company
An economic organization that produces goods or offers services; a company or business.
Sie leitet ein mittelständisches Unternehmen mit 50 Mitarbeitern.
She runs a medium-sized company with 50 employees.

undertaking
A planned, often difficult or risky project; an action or enterprise.
Die Expedition zum Nordpol war ein gefährliches Unternehmen.
The expedition to the North Pole was a dangerous undertaking.
The noun 'das Unternehmen' (company/undertaking) is derived from the verb 'unternehmen' (to undertake), which means 'to do something' or 'to tackle something'. This origin explains both meanings: a company is a large project, and an undertaking is something that one undertakes.
Die Gründung einer eigenen Firma ist ein großes Unternehmen.
Starting your own company is a major undertaking.
To distinguish the meanings, pay attention to the context. If it is about business, employees, or products, it means the company (m01). If it is about plans, adventures, or risks, it means the undertaking (m02).
Das Unternehmen investiert in neue Technologien.
The company is investing in new technologies.
In a business context, 'Unternehmen' (company) is often combined with certain verbs. Typical phrases are: 'ein Unternehmen gründen' (to found/start a company), 'ein Unternehmen leiten' (to run a company), or 'für ein Unternehmen arbeiten' (to work for a company).
Nach dem Studium möchte er ein eigenes Unternehmen gründen.
After university, he wants to start his own company.
In the meaning of 'Vorhaben' (undertaking/project), the word 'Unternehmen' is often used in a somewhat more formal or narrative style. It usually describes a larger, planned action.
Die Rettungsaktion war ein schwieriges Unternehmen.
The rescue operation was a difficult undertaking.
society / company
Both das Unternehmen and die Gesellschaft can refer to an economically active organization. Unternehmen puts the economic organization at the center, while Gesellschaft can also emphasize an economic association of people. Use Unternehmen for the organization in general and Gesellschaft when the association is the focus.

Das Unternehmen produziert Möbel und beschäftigt fünfzig Personen.
The company produces furniture and employs fifty people.
Drei Fachleute gründeten eine Gesellschaft, die Möbel produziert.
Three experts founded a company that produces furniture.