About the structure of ''There are/is''

I want to discuss the structure of ''There are/is''. First of all, what is the difference between:

There are three children.

and

Three children exist.

Do they have the same meaning?

And secondly, In my native language, we would say that

Üç çocuk vardır.

"Üç çocuk" = Three children,
"var" = existence (something that exists, a being),
and "dır" is a copula.

So basically, this structure is not different from -for example- ''three children is a car''. ''a car'' and ''existence'' have the same function. But ın English, that structure that I have mentioned is confusing for me. I know that you are all used to it. Some can say ''What's the problem with that? It is just ''there are'' and ''there is.'' ''. I realize that I still did not ask a question. Well, let me try to ask a good one, I guess.

Normally, ''there'' means a place where I am not in that place. Is there any relevance between ''there'' that means a place where I am not in that place AND ''There'' that is used in the structure of ''There are/is''? What kind of structure is this? By the way, I am new in English. Please excuse my naive usage of language. What do you think about it?

The use of the expletive there in front of a verb—usually a form of be—to assert that someone or something exists. The construction as a whole is called an ​existential sentence.

Existential there, also known as nonreferential there, is entirely different from there used as a place adverb: “It has no locative meaning, as can be seen by the contrast: There's a sheep over there. Also, existential there carries no emphasis at all, whereas the adverb does: There he is.” (Rediscover Grammar, 2003)

Examples and Observations

• There is a river that runs from Pittsburgh down into West Virginia.
• “There is a cult of ignorance in the United States.” (Isaac Asimov)

Source: https://www.thoughtco.com/existential-there-term-1690690