der Zweig
branch / twig
A smaller, woody side shoot that branches off from a branch of a tree or shrub.
Ein Vogel saß auf einem dünnen Zweig und sang.
A bird sat on a thin branch and sang.

branch
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branch / twig
A smaller, woody side shoot that branches off from a branch of a tree or shrub.
Ein Vogel saß auf einem dünnen Zweig und sang.
A bird sat on a thin branch and sang.

You can recognize the meaning of 'Zweig' (branch) from the context. If you are talking about trees or plants, the literal meaning (m01) is intended. In connection with science, art, or family, it is a subfield (m02). In the context of business or industry, it is a sector (m03).
Im Frühling bekommen die Zweige neue Blätter. (Natur)
In spring, the branches get new leaves. (nature)
In an economic context, 'Zweig' (branch) is very often the second part of a compound noun. The most common examples are 'der Wirtschaftszweig' (economic sector) and 'der Industriezweig' (industry / branch of industry).
Der Tourismus ist für viele Regionen der wichtigste Wirtschaftszweig.
Tourism is the most important economic sector for many regions.
In the figurative meaning for subfields, 'Zweig' (branch) is often used with a genitive construction: 'ein Zweig der Forschung' (a branch of research), 'ein Zweig der Literatur' (a branch of literature), or 'ein Zweig der Familie' (a branch of the family).
Er forscht in einem relativ neuen Zweig der Physik.
He conducts research in a relatively new branch of physics.
area / field
'der Bereich' and 'der Zweig' can both mean a part of a larger subject, organization, or the economy. 'Bereich' is neutral and very general. 'Zweig' emphasizes more strongly that this part branches off from something larger, like a branch on a tree. You can, for example, say 'Wirtschaftszweig' or 'ein Zweig der Medizin'. 'Bereich' fits in almost all ordinary situations. 'Zweig' sounds more precise when you mean a subcategory within a larger structure.

Im Zug liest sie einen Artikel über einen neuen Zweig der Forschung.
On the train, she is reading an article about a new branch of research.
Der Bereich Kommunikation ist für die Kundin besonders wichtig.
The communications area is especially important to the customer.