das Kätzchen
kitten
A young cat; the young animal of a cat.
Unsere Katze hat letzte Woche fünf süße Kätzchen bekommen.
Our cat had five cute kittens last week.

kitten / catkin
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kitten
A young cat; the young animal of a cat.
Unsere Katze hat letzte Woche fünf süße Kätzchen bekommen.
Our cat had five cute kittens last week.

'Kätzchen' is the diminutive form of 'die Katze' (the cat). The ending '-chen' makes the noun neuter ('das') and expresses that something is small, young, or cute.
Schau mal, da ist ein kleines Kätzchen auf der Straße!
Look, there's a little kitten on the street!
You can recognize the meaning from context: if it is about animals, it means a young cat. In connection with trees or spring, it means flowers/catkins. As a form of address for a person, it is a pet name.
Das Kätzchen spielt mit einem Wollknäuel.
The kitten is playing with a ball of yarn.
In the botanical meaning, 'Kätzchen' is often combined with 'Weide' (willow) to form 'Weidenkätzchen' (pussy willow catkin). People say that the catkins 'hängen' (hang) from the branches or 'blühen' (bloom) in spring.
Zu Ostern stellen viele Leute Zweige mit Weidenkätzchen in eine Vase.
At Easter, many people put branches with pussy willow catkins in a vase.
As a form of address, 'Kätzchen' is a very familiar and intimate pet name. It is almost always used with a possessive pronoun such as 'mein' (my) and is part of colloquial language.
Er nannte sie liebevoll ‚mein Kätzchen‘.
He affectionately called her 'my kitty'.
cat
'die Katze' and 'das Kätzchen' both refer to an animal from the cat family. The most important difference is age, and often also tone. 'Katze' is the normal word for the animal, especially when it is grown or when age is not important. 'Kätzchen' means a young cat and often sounds affectionate or cute. The words can be confused because a kitten is, of course, also a cat. If you are speaking neutrally about the animal, 'Katze' fits. If you want to emphasize that it is still young and small, 'Kätzchen' is better.

Das kleine Kätzchen trinkt noch Milch bei seiner Mutter.
The little kitten is still drinking milk from its mother.
Im Garten sitzt eine graue Katze unter dem Baum.
There is a gray cat sitting under the tree in the garden.