The word »Welt« (world) has two meanings, that are very close, but not completely identical:
everything (the universe)
The world can be the hole universe. And if we are talking about the universe, then we live inside it. And so we often also say »in der Welt«. For example:
Ich will etwas in der Welt verändern
This is: I want to change something in the world.
The world can also be just the planet Earth, and we are not living inside the planet, but on its surface. This is why we say in German
Ein Baby ist auf die Welt gekommen. Jetzt ist ein neues Kind auf der Welt.
when a baby is born. Literally: A baby did come onto the world. Now a new child is on the world.
But as far as i know, you just don't say "on the world" in english, so when you have to translate »auf der Welt« into english, you have to use the phrase »in the world«. But German »in der Welt« of course also is »in the world« in English.
There are more than one German words that originally did mean »everything that exists«. But some of them did change its meaning during the time:
This still means "everything that really is". The universe contains stars and planets as well as the planet earth, the people living on this planet, and the space between all this objects.
All ("all/everything" as a noun)
Derived from »alles« (everything). But now means "everything except the planet earth"
In the time, when this world was used first, the planet earth was identical with the universe in the peoples mind.
People in those days also had the concept of »heaven« in mind, which was a very special place. The heaven was the place where god lives, and the German world for heaven and sky is the same: Himmel. So the sky/heaven (and with it sun, moon, stars and gods living room) was a place that no living person could reach. It was undefined if this mystical place was part of world or not.
And this medieval undefinedness is the reason for the two meanings of "Welt" today.
A compound word built from »Welt« and »All«. It is a 100% synonym of »All« (Universe minus Earth)