der Ableger
offshoot
A young shoot of a plant that can be separated from the parent plant and replanted for propagation.
Ich habe von meiner Grünlilie einen Ableger für dich gemacht.
I made an offshoot from my spider plant for you.

offshoot
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offshoot
A young shoot of a plant that can be separated from the parent plant and replanted for propagation.
Ich habe von meiner Grünlilie einen Ableger für dich gemacht.
I made an offshoot from my spider plant for you.

'Der Ableger' (offshoot) derives from the verb 'ablegen' (to lay down, put aside, or deposit). In horticulture, you 'lay down' ('legt ... ab') a shoot from the parent plant in order to grow a new plant. This basic idea of splitting off from something larger is transferred to the other meanings.
Dieser kleine Kaktus ist ein Ableger von meiner großen Pflanze.
This little cactus is an offshoot of my large plant.
You can easily recognize the meaning from the context. If it is about 'Pflanzen' (plants) or 'Garten' (garden), it means a plant shoot. In the context of 'Unternehmen' (companies), 'Firma' (firm/company), or 'Organisation' (organization), it means a subsidiary. With 'Filmen' (films), 'Serien' (series), or 'Büchern' (books), it refers to a derived work (spin-off).
Meine Monstera hat schon wieder drei neue Ableger.
My monstera has already produced three new offshoots again.
In connection with plants, 'Ableger' (offshoot) is often used with the verbs 'machen' (to make), 'nehmen' (to take), or 'einpflanzen' (to plant). The preposition 'von' (from/of) describes the origin from the parent plant.
Kannst du mir einen Ableger von deiner schönen Rose machen?
Can you make me an offshoot from your beautiful rose?
When referring to a subsidiary, typical verbs are 'gründen' (to found) or 'eröffnen' (to open). The affiliation is often expressed with 'von' (of/from) or a genitive.
Das Technologieunternehmen plant einen Ableger in Berlin.
The technology company is planning a branch in Berlin.
In this meaning, 'Ableger' (spin-off/offshoot) is often used disparagingly or critically. Common combinations are 'ein billiger Ableger' (a cheap spin-off), 'ein schwacher Ableger' (a weak spin-off), or 'nur ein Ableger von etwas sein' (to be only a spin-off of something).
Viele Fans waren enttäuscht und nannten den Film einen seelenlosen Ableger.
Many fans were disappointed and called the film a soulless spin-off.
successor
'der Nachfolger' and 'der Ableger' can both refer to something that comes after something else or develops from something else. The important difference is: a 'Nachfolger' usually replaces an earlier person, product, or version. An 'Ableger' develops from a larger organization, brand, or model, but normally does not replace it. So an 'Ableger' can continue to exist alongside the original. The words can be especially easy to confuse when talking about companies, films, or products. If something replaces the old version, 'Nachfolger' fits better. If something comes out of the original and continues independently, 'Ableger' fits better.

Der Streamingdienst plant einen Ableger der bekannten Serie.
The streaming service is planning a spin-off of the well-known series.
Das neue Modell ist der Nachfolger des alten Handys.
The new model is the successor to the old phone.