
bäuerlich
rural
Relating to farmers, agriculture, or life in the countryside; in the style of farmers.
Wir verbrachten den Urlaub in einer Pension mit bäuerlichem Charme.
We spent our vacation in a guesthouse with rural charm.
rural / peasant-like
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rural
Relating to farmers, agriculture, or life in the countryside; in the style of farmers.
Wir verbrachten den Urlaub in einer Pension mit bäuerlichem Charme.
We spent our vacation in a guesthouse with rural charm.

peasant-like
Derogatory: coarse, unpolished, or rough in behavior.
Seine bäuerlichen Tischmanieren stießen in der feinen Gesellschaft auf Ablehnung.
His peasant-like table manners were met with disapproval in polite society.
The adjective 'bäuerlich' (rural, peasant-like) is derived directly from the noun 'der Bauer' (the farmer). It describes things that are typical of farmers or country life.
Das Restaurant ist im bäuerlichen Stil eingerichtet.
The restaurant is decorated in a rural style.
In its neutral or positive meaning, 'bäuerlich' (rural) is often connected with aspects of country life. Common combinations are 'bäuerliche Idylle' (rural idyll), 'bäuerliche Produkte' (farm products), or 'ein bäuerlicher Betrieb' (a farm operation).
Auf dem Markt kann man frische bäuerliche Erzeugnisse kaufen.
At the market you can buy fresh farm products.
When 'bäuerlich' (peasant-like) describes behavior or manners, it has a derogatory meaning and means 'coarse' or 'uncultivated'. The context makes the negative judgment clear.
Sein lautes Rülpsen bei Tisch wurde als bäuerliches Benehmen empfunden.
His loud burping at the table was seen as peasant-like behavior.
rural
Ländlich generally describes a place or way of life outside the city. Bäuerlich, on the other hand, emphasizes a connection with farmers, agriculture, or their way of life. Ländlich is suitable for a village without any particular connection to agriculture; bäuerlich is more appropriate for a farm or a way of life shaped by agriculture.

Der aktive Bauernhof mit seinen Ställen ist deutlich bäuerlich geprägt.
The working farm, with its barns, is distinctly agricultural in character.
Das kleine Dorf mit seinen ruhigen Straßen ist deutlich ländlich geprägt.
The small village, with its quiet streets, is distinctly rural in character.