die Einrichtung
furnishings
The collection of furniture, rugs, lamps, and other objects in a room or apartment.
Die neue Wohnung hat eine sehr helle und moderne Einrichtung.
The new apartment has very bright and modern furnishings.

furnishings / institution / setup
Loading your saved state.
furnishings
The collection of furniture, rugs, lamps, and other objects in a room or apartment.
Die neue Wohnung hat eine sehr helle und moderne Einrichtung.
The new apartment has very bright and modern furnishings.

'Die Einrichtung' (furnishings/institution/setup) is the noun related to the separable verb 'einrichten' (to furnish/set up). The verb means to put furniture in a room or to install something technically. The noun describes the result or the process of this action.
Wir müssen das neue Büro noch komplett einrichten.
We still have to furnish the new office completely.
You can recognize the meaning from the context: if it is about furniture and style, it refers to the furnishings of an apartment. If it is about organizations like schools or offices, it means an institution. If it is about technology or accounts, it means the setup or installation process.
Ihre Einrichtung ist sehr geschmackvoll.
Her furnishings are very tasteful.
When it is about furniture and decoration, 'Einrichtung' is often combined with adjectives that describe a style, e.g. 'moderne' (modern), 'klassische' (classic), 'gemütliche' (cozy), or 'komplette' (complete) furnishings.
Sie wünscht sich eine helle und moderne Einrichtung für ihr Wohnzimmer.
She wants bright and modern furnishings for her living room.
As an institution, 'Einrichtung' is often further specified with adjectives such as 'öffentlich' (public), 'sozial' (social), 'staatlich' (state-run), or 'medizinisch' (medical).
Das Krankenhaus ist eine wichtige medizinische Einrichtung in der Stadt.
The hospital is an important medical institution in the city.
In the meaning 'Setup/Installation', a genitive or 'von' + dative is often used to specify what is being set up. For example: 'die Einrichtung des Kontos' (the setup of the account) or 'die Einrichtung von dem neuen Programm' (the setup of the new program).
Die Einrichtung des neuen WLAN-Routers dauerte nur wenige Minuten.
Setting up the new Wi-Fi router took only a few minutes.
organization
'die Organisation' and 'die Einrichtung' can both refer to a fixed place or body where people work for a particular purpose. 'Organisation' puts more emphasis on the group, its goals, and its structure. 'Einrichtung' is often used for a concrete institution that serves a public, social, or economic purpose, for example a school, a hospital, or a care home. Learners may confuse the words because many 'Einrichtungen' are also organizations. 'Organisation' sounds more appropriate when the focus is on the group and its work; 'Einrichtung' sounds more natural when you mean the institution as a place or service.

Gibt es in der Nähe eine Einrichtung für ältere Menschen?
Is there an institution for older people nearby?
Mein Kollege arbeitet für eine Organisation, die Nachbarn im Alltag hilft.
My colleague works for an organization that helps neighbors in everyday life.