der Spross
sprout
A young shoot or bud growing from a plant.
Im Frühling sieht man an den Bäumen die ersten grünen Sprosse.
In spring, you can see the first green sprouts on the trees.

sprout / offspring
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sprout
A young shoot or bud growing from a plant.
Im Frühling sieht man an den Bäumen die ersten grünen Sprosse.
In spring, you can see the first green sprouts on the trees.

The noun 'der Spross' (sprout/offspring) is closely related to the verb 'sprießen' (to sprout), which means 'to grow out of the ground or a plant.' A Spross is therefore something that sprouts.
Nach dem Regen sprießen überall kleine, grüne Sprosse aus der Erde.
After the rain, small green sprouts are sprouting from the ground everywhere.
You can easily recognize the meaning from the context. If people are talking about plants, trees, or vegetables, it means the young shoot. If it is about families, noble houses, or dynasties, it means a descendant.
Die Bambussprosse sind ein wichtiger Teil der asiatischen Küche.
Bamboo shoots are an important part of Asian cuisine.
In the meaning of 'Nachkomme' (descendant), 'Spross' (offspring) is used more in an elevated, slightly literary, or ironic style. It is not a neutral everyday word for 'Kind' (child).
Die Zeitung berichtete über den neuesten Spross der königlichen Familie.
The newspaper reported on the newest offspring of the royal family.
'Spross' (offspring) is often used with a genitive or the preposition 'von' (of/from) to make the origin clear. A very typical combination is 'der jüngste Spross von/einer Familie' (the youngest offspring of a family).
Er ist der jüngste Spross einer alten Industriedynastie.
He is the youngest offspring of an old industrial dynasty.
child
'das Kind' and 'der Spross' can both mean a descendant in a family. 'Kind' is the normal word for a son or daughter and fits in almost all everyday situations. 'Spross' sounds more elevated, more figurative, or sometimes slightly humorous. It can also mean a child or grandchild of a family. Learners may confuse the words because both express a family relationship. In everyday language, people usually say 'Kind'. 'Spross' is more suitable in reports, stories, or when you deliberately want to speak in a more figurative way.

Der jüngste Spross der Familie beginnt im Herbst eine Ausbildung.
The youngest offspring of the family is starting an apprenticeship in the fall.
Ihr Kind kommt heute früher aus der Schule nach Hause.
Her child is coming home from school earlier today.