Everyone is both a bit right and wrong here, depending on the exact things that is done where and how; and from the perspective of OP it doesn't really matter really matter beyond:
No, you are not downloading/copying 20 gigs in 3 seconds.
Computers do a lot of smart stuff to not actually have to move data around unless absolutely necessary; and there are many techniques involved here.
For instance:
When copying a big file it might look to an average user as if they have two files, but in fact it could just be one file that you can access from two different places.
This could happen in such a way that changes from one place will be shown also from the other place; which is how we think of how a file alias works.
But it could also be such that you have one file, but the second copy isn't actually created until it's being manipulated from the second place. So it looks like two files, and acts like two files; but the actually copy isn't created until it's actually needed.
A third way could be that there is one file, accessible from two places; but the changes made from one place is saved separately. So it looks and acts like two files; but internally it's more like one core file, and then diff data.
And I could go on with more versions of this, and it could be implemented at different layers; all the way from deep down in the filesystem itself, up to the app that you're using.
When you on top of that also use some sort of well integrated cloud syncing/storage things get even more complicated; but generally speaking it should all the pretty much invisible to the average Mac user. The only problem could be if you think you have the data on your laptop, and then try to use it without internet access.