die Welt
world
The planet Earth with all its countries, seas, and living beings.
Sie möchte nach dem Studium um die Welt reisen.
She wants to travel around the world after her studies.

world
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world
The planet Earth with all its countries, seas, and living beings.
Sie möchte nach dem Studium um die Welt reisen.
She wants to travel around the world after her studies.

'Welt' (world) is a very productive word and forms many important nouns. Examples include 'Weltreise' (trip around the world), 'Weltmeister' (world champion), or 'Weltall' (universe/space).
Deutschland wurde 2014 Fußball-Weltmeister.
Germany became football world champion in 2014.
When 'Welt' means the planet Earth, it is often used in fixed expressions. Typical examples are 'um die Welt reisen' (to travel around the world), 'auf der ganzen Welt' (all over the world), and 'in aller Welt' (in the whole world/around the world).
Dieses Produkt wird auf der ganzen Welt verkauft.
This product is sold all over the world.
When 'Welt' describes a specific field, it is almost always followed by a specification with the genitive or with 'von' (of). This structure ('die Welt der/des...' or 'die Welt von...') is a clear signal for this meaning.
Sie ist eine Expertin in der Welt der klassischen Musik.
She is an expert in the world of classical music.
In the metaphorical meaning, 'Welt' follows a fixed pattern: 'Etwas bedeutet jemandem die Welt' (something means the world to someone). The person for whom something is important is always in the dative.
Seine Familie bedeutet ihm die Welt.
His family means the world to him.
The expression 'zur Welt kommen' is a fixed phrase for 'geboren werden' (to be born). Another fixed expression is 'etwas zur Welt bringen', which means 'to give birth to a child'.
Meine Nichte ist gestern gesund zur Welt gekommen.
My niece was born healthy yesterday.
The expressions 'die ganze Welt' (the whole world) or 'alle Welt' (everyone/the whole world) are often used as hyperbole (exaggeration). They then do not literally mean all people on Earth, but simply 'very many people' or 'the public'.
Alle Welt spricht über den neuen Film.
Everyone is talking about the new film.
society / company
'die Welt' and 'die Gesellschaft' can both refer to people as a group. 'Welt' is broader and often more general: it can mean many people or the public, and sometimes even all people. 'Gesellschaft' refers more to the people who live in a shared social system, with rules, roles, and problems. The words can be confused because both talk about people. When it is about public attention, 'Welt' often fits. When it is about living together, social issues, or rules, 'Gesellschaft' is more precise.

Die ganze Welt spricht über das große Sportereignis.
The whole world is talking about the major sporting event.
Nico findet, dass die Gesellschaft mehr für ältere Menschen tun sollte.
Nico thinks that society should do more for older people.