syntactic analysis - 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?

Answer

I think you are referring to the 'existential there' (sometimes 'nonreferential there').

There's a useful link here:
https://www.thoughtco.com/existential-there-term-1690690