Shredder1511
Everything in the Third Party section of the Software Center is downloaded directly from upstream, in this case that would be Google. Software in the Third Party section requires you to update them manually by clicking check for updates for each third party item installed.
Why is the third party system different?
My understanding is all the software in the Third Party section has a restrictive license that prevent them being distributed, in other words Solus can not legally host the binary package in the repository with all the rest of the software.
For Google Chrome its downloading the .deb file provided by google and repackages it into an .eopkg on the users system which it then installs. Doing it this way means Solus is abiding by the license and the end user doesn't need to understand how packaging works.
https://github.com/getsolus/3rd-party/blob/master/network/web/browser/google-chrome-stable/pspec.xml
This system isn't entirely automated and every time a new version is released someone has to go and update the pspec.xml I just linked to.
If you wanted to install software in the third party section via the terminal you can:
https://getsol.us/articles/software/third-party/en/