Okay. Too bad there is no way to put "[SOLVED]" in the thread title.
Of course, there are about a zillion ways to get what you want here.
Likewise, there are a many variables that can abruptly bork your desired method if you innocently change a seemingly harmless setting or change a preference during a download (or if a website suddenly decides to provide its own PDF viewer):
- Chrome has a built-in PDF viewer which is turned on by default;
- Windows 10 evidently has a "system" PDF viewer (you might have mistaken the Chrome PDF viewer for the Windows "system" viewer);
- You can set Chrome to just download PDFs to your drive, and not open them in a PDF reader;
- You can set a default PDF viewer for Windows 10;
- You can set a default PDF viewer for the Chrome browser;
- There are browser add-ons/extensions that open PDF files;
- Additionally, the PDF viewer shown in the image that you posted lives on Brisnet, if you don't want it to appear, you might have to bypass it with a Chrome extension (NoScript, uBlockOrigin, etc.) or you could possibly change your default download settings in Chrome.
If it were me, I would just go to the settings within Chrome (not in Windows 10) and set your desired PDF reader to Foxit. Then, instead of "saving" the file to your drive, set the Chrome default to always open PDFs in Foxit (sounds like this is what is happening now). Then just save the PDF file while in Foxit before you close it.