das Gebiet
area
A specific geographical area, region, or territory.
Dieses Naturschutzgebiet ist die Heimat seltener Vogelarten.
This nature reserve is home to rare bird species.

area / field
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area
A specific geographical area, region, or territory.
Dieses Naturschutzgebiet ist die Heimat seltener Vogelarten.
This nature reserve is home to rare bird species.

'Das Gebiet' (area/field) is related to the verb 'gebieten' (to rule or command). So a 'Gebiet' was originally an area over which someone rules or that is clearly delimited.
Der König herrschte über ein riesiges Gebiet.
The king ruled over a huge territory.
The preposition reveals the meaning: 'in einem Gebiet' (in an area) refers to a geographical place. 'Auf einem Gebiet' (in a field) refers to a specialist or knowledge area.
In diesem Gebiet gibt es viele seltene Pflanzen.
There are many rare plants in this area.
The word 'Gebiet' (area) is often the second part of compound nouns that describe a particular type of region. Examples are 'Naturschutzgebiet' (nature reserve), 'Industriegebiet' (industrial area), or 'Wohngebiet' (residential area).
Am Stadtrand entsteht ein neues Wohngebiet.
A new residential area is being built on the outskirts of the city.
In the context of knowledge, 'Gebiet' (field) is often combined with words like 'Experte' (expert), 'Spezialist' (specialist), 'Forschung' (research), or 'Kenntnisse' (knowledge). A typical formulation is 'ein Experte auf dem Gebiet von ...' (an expert in the field of ...).
Sie ist eine führende Spezialistin auf dem Gebiet der Genetik.
She is a leading specialist in the field of genetics.
world
'die Welt' and 'das Gebiet' can both refer to a space or an area. But 'die Welt' is much larger or more figurative: it can mean the whole planet or an entire area of life or field, for example 'die Welt der Musik' (the world of music). 'das Gebiet' is more clearly limited. It works for a specific region on a map or for a specific field. Learners may confuse the words when talking about subject areas. As a simple guide: 'Welt' sounds broader and more vivid, while 'Gebiet' sounds more precise and factual.

Wegen der Bauarbeiten darf die Gruppe dieses Gebiet morgen nicht betreten.
Because of the construction work, the group is not allowed to enter this area tomorrow.
In der Welt der Mode ändern sich die Trends sehr schnell.
In the world of fashion, trends change very quickly.