vegetarisch
vegetarian
Prepared without meat or fish; relating to a diet in which meat and fish are not eaten.
In diesem Restaurant gibt es viele leckere vegetarische Gerichte.
There are many delicious vegetarian dishes in this restaurant.

vegetarian
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vegetarian
Prepared without meat or fish; relating to a diet in which meat and fish are not eaten.
In diesem Restaurant gibt es viele leckere vegetarische Gerichte.
There are many delicious vegetarian dishes in this restaurant.

The ending '-isch' is a very common suffix in German for forming adjectives. It often expresses belonging or a quality, as here with 'vegetarisch' (vegetarian).
Aus ethischen Gründen isst sie nur vegetarische Produkte.
For ethical reasons, she eats only vegetarian products.
'Vegetarisch' (vegetarian) is often combined with food and lifestyle. Common collocations are: 'ein vegetarisches Gericht' (a vegetarian dish), 'eine vegetarische Ernährung' (a vegetarian diet), 'eine vegetarische Lebensweise' (a vegetarian lifestyle), or 'vegetarische Wurst' (vegetarian sausage).
Immer mehr Menschen interessieren sich für eine vegetarische Ernährung.
More and more people are interested in a vegetarian diet.
You can describe both dishes and lifestyles as 'vegetarisch' (vegetarian). A person themselves is not 'vegetarisch'; rather, they 'lebt vegetarisch' (live as a vegetarian) or 'ernährt sich vegetarisch' (eat a vegetarian diet).
Dieses Curry ist vegetarisch, es ist ohne Fleisch gekocht.
This curry is vegetarian; it is cooked without meat.
vegan
'vegan' and 'vegetarisch' both describe food or a diet without meat and fish. The difference is: 'vegetarisch' often allows milk, eggs, or honey; 'vegan' does not. 'vegan' can also refer to an entire lifestyle, for example without leather or wool. Learners easily confuse the words because both have to do with avoiding meat. If it is only about having no meat and no fish, 'vegetarisch' fits. If there are no animal products at all, 'vegan' is more precise.

Meine Mutter isst vegetarisch, aber Käse und Joghurt mag sie sehr.
My mother eats vegetarian food, but she really likes cheese and yogurt.
Für die Feier backt Lisa einen veganen Kuchen ohne Milch und Eier.
For the party, Lisa is baking a vegan cake without milk or eggs.