biologisch
biological
Relating to biology, the study of living beings and life processes.
Alterung ist ein komplexer biologischer Prozess.
Aging is a complex biological process.

biological / organic
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biological
Relating to biology, the study of living beings and life processes.
Alterung ist ein komplexer biologischer Prozess.
Aging is a complex biological process.

The adjective 'biologisch' (biological / organic) is derived from the noun 'die Biologie' (biology). The ending '-isch' is often used to form adjectives from scientific or technical terms.
Die psychologische Wirkung von Farben ist gut erforscht.
The psychological effect of colors is well researched.
You can recognize this meaning from the scientific or medical context. Typical nouns here are 'Prozess' (process), 'Merkmal' (feature/trait), 'System' (system), or 'Waffen' (weapons).
Das Immunsystem ist ein hochkomplexes biologisches System.
The immune system is a highly complex biological system.
This meaning is used in connection with food, agriculture, and shopping. Pay attention to nouns like 'Anbau' (cultivation), 'Landwirtschaft' (agriculture), 'Produkt' (product), or 'Lebensmittel' (food).
Immer mehr Supermärkte bieten biologische Produkte an.
More and more supermarkets offer organic products.
In everyday language, the short form 'Bio-' is very often used as a prefix instead of the full adjective. For example, people speak of 'Bio-Eiern' (organic eggs), a 'Bio-Bauernhof' (organic farm), or a 'Bio-Laden' (organic shop).
Ich kaufe mein Gemüse am liebsten auf dem Bio-Markt.
I prefer to buy my vegetables at the organic market.
This meaning refers to blood relations and is used in the context of family and descent. It often comes before nouns like 'Eltern' (parents), 'Mutter' (mother), 'Vater' (father), or 'Geschwister' (siblings).
Er kennt seinen biologischen Vater nicht.
He does not know his biological father.
natural / of course
'natürlich' and 'biologisch' can both refer to products that do not seem strongly artificial or that come from nature. The difference is important: 'natürlich' is general and only says that something comes from nature or does not seem artificially changed. 'biologisch' is more specific and, with food or agriculture, means that something was produced according to organic standards. Learners may confuse the words because both sound healthy or connected to nature. But not every natural product is automatically organic.

Mila hat auf dem Markt biologische Äpfel gekauft.
Mila bought organic apples at the market.
Julia kauft einen natürlichen Saft ohne künstliche Aromen.
Julia buys a natural juice without artificial flavorings.