das Departement
administrative district
An administrative unit or district in certain countries, especially in France and Switzerland.
Paris liegt im Departement Île-de-France.
Paris is located in the Île-de-France department.

department / administrative district
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administrative district
An administrative unit or district in certain countries, especially in France and Switzerland.
Paris liegt im Departement Île-de-France.
Paris is located in the Île-de-France department.

'Departement' (department) is a loanword from French. This influences the pronunciation and points to the origin of the concept, especially for administrative districts.
Die Weinregion Bordeaux liegt im Departement Gironde.
The Bordeaux wine region is located in the Gironde department.
The context makes the meaning clear: If it is about geography, countries, or administration (especially in France), it means a district. If it is about universities, ministries, or companies (especially in Switzerland), it means a department.
Jedes Schweizer Ministerium wird als Departement bezeichnet.
Each Swiss ministry is referred to as a department.
As a term for a department in an organization, 'Departement' (department) is very common especially in Switzerland (e.g., at universities or in government). In Germany, this use is less common.
Sie ist Professorin am Departement für Geschichte der Universität Basel.
She is a professor in the Department of History at the University of Basel.
district
'der Landkreis' and 'das Departement' can both be administrative units, but they fit different countries and contexts. 'Landkreis' is used mainly in Germany and Austria for an area that includes several municipalities. 'Departement' is used for certain countries such as France or Switzerland. In addition, 'Departement' can also mean a department within an organization, for example at a university. The words can be confusing because both have to do with administration or structure. For German administration, 'Landkreis' is usually correct; 'Departement' only sounds natural in suitable foreign or organizational contexts.

In Frankreich liegt die Stadt in einem Departement nahe der Küste.
In France, the town is located in a department near the coast.
Der Landkreis plant eine neue Buslinie zwischen den Dörfern.
The district is planning a new bus route between the villages.