Borderless PDF saving from website
It sounds like the border is a part of the PDF document itself, in which case it's not an issue with printing preferences. The easiest solution is to crop the PDF in Preview, then print it.
Instead of File &gt; Print, perform File &gt; Export as PDF (or Save as).
Open the PDF in Preview and crop it.
From the above Apple support article:

If the Markup toolbar isn’t showing, click the Show Markup Toolbar
button , then click the Rectangular Selection button .
Select the portion of the page you want to keep.
Click the Crop button in the Markup toolbar (or use the Touch Bar).

Once you select the portion, you can alternatively the shortcut command + K to crop it as well.
Once you are finished, save the PDF if you wish and print it.