You need to right click on the pdf showing the firefox icon and you should have an option to open with. Then you should be able to pick Adobe. Another way is to look up default apps and then find .pdf, then change it to Adobe. I'm not on windows right now, but it should be a simple change.

AI Overview.

No, I was not clear enough. On both PCs, Firefox is the default for opening PDFs - as I prefer. However, the icons displayed differ on the two PCs.

On one PC, a generic PDF icon is displayed for PDF files. The type of file shown in properties for these is "FIrefox PDF Document."

On the second PC. the usual Firefox browser icon is displayed. The type of file shown in properties for these is "PDF file."

Do I need to switch to another application for opening PDFs first and then change to have Firefox as the default?

You should be able to change the icon in the properties.

Compare what they are set to open with.

No option is available to change the icon in properties, even under advanced attributes.

Just spent some time in Windows.... Looks like you can only change what you open with on files to get the icon to change, but on shortcuts you can change the icon. Make a shortcut to file and then in the properties you will see the change icon option.

On the first PC, Firefox shows up twice in the list of applications. Selecting the first Firefox icon opens the file in a new tab in the currently open Firefox browser window.

 This is the expected result.

Selecting the second Firefox icon opens a new file on the desktop and asks about making Firefox the default, which I had done before and did again.

 This is not anything I had seen before but it appears to work with the usual editing capabilities

Both Firefox icons remain on the "Open with" list on the first PC and subsequent selection results are unchanged.

Show it.

See attached image of same file opened with each of the two Firefoxes

The Windows issue is that the icons are different. I was looking for a screenshot showing the icons and not the files open.

See the icon images. Any pdf file is stored showing the PDF icon.