Yes, it's called a print server.

Yes, and it's called a print server, as others said. FWIW, CUPS have a "virtual PDF printer" which enables "Print to PDF" feature system wide, so no application has to reimplement it.

Also, I used to use a "PDF printer" in the olden days on Windows which did exactly that, and that was considered a paid, premium product.

IOW, we have these. Both in personal and enterprise flavors, for a long time.

They are asking for a physical device with a memory card, that you attach to your computer and it appears as a printer to the computer and when you print to it, the device instead creates a PDF on its memory card. I think.

I also first started typing a comment about “PDF printer” software that I used to use on Windows XP back in the day before most programs and before Windows had a native export to PDF via print dialog. (These days I run macOS. So not sure if current Windows has export to PDF at system level when you print from any program. I know Office has built in export to PDF, and I think back in the day Office did not have that.)

> ... for a physical device with a memory card, that you attach to your computer and it appears as a printer to the computer and when you print to it, the device instead creates a PDF on its memory card. I think.

Actually, it doesn't matter. Install an operating system to any computer (from OrangePi Zero to a CRAY-1, doesn't matter), install a "virtual" PDF printer and share from the network. It'll appear as a printer. It'll print to a folder local to that machine, not yours. It's again the same thing (this is the magic of the network, actually).

IIRC from administering my parents' Windows PC, the OS now has Print to PDF capability built-in, but IDK whether that virtual printer is installed with Office, but it's out of the box.