do wirelss printers require wifi

My wireless printer shows up on my debian.ubintu/caelinux and android devices, but they don't seem to know to print to it.

Must I get a wifi router?

Gotta have a wifi network to talk to a device over WiFi...

Some models *may* offer their own WiFi or NFC network for "WiFi Direct" printing. Check your manual.

Depends on the printer. Read its manual. Does it support ad-hoc WiFi?

Then you need to publish all diagnostics and information you have on the problem, we can not help otherwise.

This is off-topic here, anyway. You should ask in a Linux group for learning how to print on Linux, how to connect a particular printer to it.