der Muffin
muffin
A small, sweet baked good in the shape of a cake, often filled with fruit, nuts, or chocolate and baked in a paper cup.
Zum Kaffee bestellte sie sich einen Schokoladen-Muffin.
She ordered a chocolate muffin with her coffee.

muffin
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muffin
A small, sweet baked good in the shape of a cake, often filled with fruit, nuts, or chocolate and baked in a paper cup.
Zum Kaffee bestellte sie sich einen Schokoladen-Muffin.
She ordered a chocolate muffin with her coffee.

The word 'Muffin' (muffin) usually refers to the small, sweet baked good. The second meaning, a flat yeast bread, is less common and is often made clearer by context such as 'toasten' (to toast) or 'belegen' (to top/fill), or by the term 'English Muffin' (English muffin).
Ich hätte gern einen Kaffee und einen Muffin.
I'd like a coffee and a muffin.
To describe the type of sweet baked good, a compound word is often formed. Typical examples are 'Schokoladen-Muffin' (chocolate muffin), 'Blaubeer-Muffin' (blueberry muffin), or 'Zitronen-Muffin' (lemon muffin).
Im Café gibt es heute frische Blaubeer-Muffins.
The café has fresh blueberry muffins today.
In connection with the sweet baked good, the verbs 'backen' (to bake) and 'essen' (to eat) are often used.
Am Wochenende backen wir oft zusammen Muffins.
On the weekend, we often bake muffins together.
cake
'der Kuchen' and 'der Muffin' are both sweet baked goods and can taste similar. The most important difference is their shape and size. A cake is usually larger and cut into pieces. A muffin is small, round, and often baked in a paper cup. You can think of a muffin as a small cake-like baked good, but in everyday language you would not simply call it 'Kuchen' if you want to be precise. The words can be confused because both are baked from batter or dough and often contain chocolate, fruit, or nuts.

Beim Frühstück nimmt Sarah einen Muffin mit Schokolade.
At breakfast, Sarah has a muffin with chocolate.
Das Team isst Kuchen, weil eine Kollegin Geburtstag hat.
The team is eating cake because a colleague has a birthday.