You click a PDF link expecting a file and get a browser tab instead. That does not establish whether a usable local copy exists. Firefox’s action for PDF downloads and its download location are separate settings.
Change the action for PDF
In desktop Firefox, open Settings and find the list of file types and applications. Depending on the version, Mozilla places it under General or the Downloads panel. Find Portable Document Format (PDF), then inspect its action: open in Firefox, save, ask each time or use an available application.
Choose the behaviour you need for future PDF downloads. If you only want this document, use the PDF viewer’s download control instead of changing a global setting. An absent file-type entry or a website’s delivery instructions can affect what options apply; not every link follows the same route.
Keep the folder decision separate
“Save file” answers what to do with the content. The download folder answers where to put it. Check the configured destination or the option to ask for a location. Choosing an external viewer can still save a file in the Downloads folder; opening is not proof that nothing was stored.
This Firefox setting does not decide which browser Windows opens when you click an ordinary web link. That is a separate default-app association.
Verify one harmless document
Try a public PDF you already trust. Open Firefox’s downloads list, locate the file and open the local copy. Check its name, page count and content rather than relying on a notification. If a website serves an HTML page with “PDF” in its name, changing a filename extension will not convert it. When the choice is wrong, restore the previous PDF action; there is no need to reset every browser setting.