@Finntendo

You should read the Docs.
Here you can find many answers to your questions.

I will try to answer your question.

RetroPie is a collection of bash scripts running on top of a lite linux OS.
Lite means it has no Desktop (windows) environment it only has the terminal.
You can even install RetroPie separately on your own compatible debian based linux OS, even if it has a Desktop environment, even if it's not a Raspberry Pi.

Just see a binary as an EXE files from windows, it is also a binary, you download it and it runs.
But to create EXE files you need to compile it first from source so the computer can understand it.
Compiling is converting the programming language into understandable code for the CPU this can take a long time depending on what computer you use.

The RetroPie guys made it easier by supporting binary installs for the Raspberry Pi and perhaps for some other arm boards.
They compiled it for you and many people can use them.

Source installs can be more up to date if the source code is maintained regularly and the binary files are behind but it takes much more time to install.
Though the binaries from RetroPie are updated quite regularly so if it's possible to update from binary than that is in most cases a better choice as it is much faster.

You say you have updated everything now from source.
This means that all installs are very up to date.
So when everything works I would wait some time to update from binary.
Because it could mean that you downgrade the emulators.

The OS underlying files are updated in a quite normal way.
This does not depend on the source / binary installs.
So you won't downgrade your OS.

What is this screen?