This is what has been happening for a while if you have “Open in Firefox” selected as your PDF handling preference (that is the default setting):
(A) If the server accurately identified the PDF using “Content-Type: application/pdf” and did NOT send the “Content-Disposition: attachment” header to force downloading:
Firefox saves the file in the web content cache and opens the PDF with the web address showing in the address bar.
(B) If the server accurately identified the PDF using “Content-Type: application/pdf” and DID send the “Content-Disposition: attachment” header to force downloading:
Firefox saves the file in the folder you selected next to “Save files to:” on the Settings page and opens it in a new tab with the local path (file:/// ) showing in the address bar.
Firefox 102 added a preference that allows switching from the “Save files to:” folder to the Temp folder.
© Other situations…
Firefox sometimes takes the .pdf extension at face value when sites try to sneak it past using inaccurate Content-Type values (such as “Content-Type: application/force-download”). In that case, it may follow behavior (B). Otherwise, it may auto-save the file.