Can a wireless printer differentiate between two of the same model printers?

I just got a new wireless printer that happened to be on sale and works well so I gave my old wired one to my dad because it still worked well. It turns out that it was too old to run with his computer, so he wants to buy a wireless printer as well. He would love to get the same one he got me because it was at a good price, but he's not sure if when he chose to print something would it be sent to both printers, or was there a way to pick which of the wireless printers to go even if they are the same kind of printer. Any thoughts or details you need?