It depends... With Word documents and other kinds of content that Firefox doesn't know how to display, Firefox will save the file so you can open it in another app. You have more options with PDF files. So assuming that PDFs are the problem, let me describe some possible fixes.

Using the Open in Firefox option

Firefox can't display PDFs in a tab without downloading and saving them somewhere. You can tweak some hidden settings to determine where Firefox saves the file, whether that is the web content cache, the "Save files to:" download folder, or the Windows Temp folder. Here are the slightly messy details.

Background: inline vs. attachment disposition

If web servers don't specify how Firefox should handle a PDF, or if they specify "inline" handling, then then Firefox loads the PDF as web content with its original URL in the address bar. The PDFs are saved with other cached web content, not in your download folder. This is good.

But web servers can try to force a download by setting Content-Disposition: attachment if they don't want browsers to show the files in a tab. In that case, Firefox saves the file and then opens it with a file:// address.

Options for saving PDF downloads

(1) Just for PDFs, override "attachment" disposition to "inline"

When your handling action is "Open in Firefox", all PDFs can now be opened as web content and saved in the cache instead of a regular folder. Here's how you set this up:

(a) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

More info on about:config: Configuration Editor for Firefox. The moderators would like us to remind you that changes made through this back door aren't fully supported and aren't guaranteed to continue working in the future. I'm using this so I feel comfortable mentioning it.

(b) In the search box in the page, type or paste browser.download.open_pdf_attachments_inline and pause while the list is filtered -- requires Firefox 103 or later

(c) Double-click the preference to switch the value from false to true

(2) For all the downloads Firefox saves to disk and opens automatically, change from the "Save files to" folder to the Windows Temp folder (if you made the change in #1, this will affect other kinds of files rather than PDFs)

This will allow Windows to clean up the downloads and they won't clutter your Downloads folder. Here's how you access it:

(a) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

More info on about:config: Configuration Editor for Firefox. The moderators would like us to remind you that changes made through this back door aren't fully supported and aren't guaranteed to continue working in the future.

(b) In the search box in the page, type or paste browser.download.start_downloads_in_tmp_dir and pause while the list is filtered -- requires Firefox 102 or later

(c) Double-click the preference to switch the value from false to true

This would not affect files opened with inline disposition; those will still be in the web content cache.

Hopefully some of that gets Firefox working the way you want.

It may help to check your choices for the files in Settings → General → Files and Applications → Applications. They may be set to Open in Firefox. I find from time to time that some of 'my' choices have been changed without my volition.