badisch
from Baden
Refers to the region of Baden in southwestern Germany, its inhabitants, its culture, or its dialect.
Er bestellte ein Glas badischen Wein zum Essen.
He ordered a glass of wine from Baden with his meal.

Baden
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from Baden
Refers to the region of Baden in southwestern Germany, its inhabitants, its culture, or its dialect.
Er bestellte ein Glas badischen Wein zum Essen.
He ordered a glass of wine from Baden with his meal.

The adjective 'badisch' (from Baden) is derived from the region 'Baden'. The ending '-isch' is a typical way to form adjectives from geographic names.
Die badische Weinstraße ist ein beliebtes Ausflugsziel.
The Baden Wine Route is a popular excursion destination.
Adjectives derived from geographic names with the ending '-isch' are written in lowercase in German. So you write 'badischer Wein' (wine from Baden), not 'Badischer Wein'.
Ich mag die badische Küche sehr gerne.
I really like Baden cuisine.
'Badisch' (from Baden) is often used in connection with regional specialties and cultural terms, for example 'badischer Wein' (wine from Baden), 'badische Küche' (Baden cuisine), or 'badischer Dialekt' (Baden dialect).
Meine Großmutter spricht noch den alten badischen Dialekt.
My grandmother still speaks the old Baden dialect.
Swabian
'schwäbisch' and 'badisch' both refer to regions in southwestern Germany, but to different regions. 'schwäbisch' belongs to Swabia and can also refer to the Swabian dialect. 'badisch' belongs to Baden, its people, its culture, or its dialect. The words are easy to confuse because Baden and Swabia are geographically close to each other and both are often connected with Baden-Württemberg. For people from the region, the difference is important. So you should not simply use both words for the same place.

In der Schule hat Finn erzählt, dass seine Großeltern badisch sprechen.
At school, Finn said that his grandparents speak the Baden dialect.
Sie spricht schwäbisch, wenn sie mit ihrer Familie telefoniert.
She speaks Swabian when she talks to her family on the phone.