When you use invoicePlane, PHP code run on a distant server. So printing would be made on a printer attached to this server.
PHP code generates a PDF file that is sent to your browser
Client side (your browser)
You display this PDF file either in your browser, either via utility like AcrobatReader. Now, you can print it ([ctrl] P) to any printer connected to YOUR computer using you OS driver which is on charge of the rendering on paper.
Labelling printers come generaly with proprietary applications which doesn’t use a driver (direct printing) but you can install one.