Do I need a phone cord from Apple TV box to internet box?

If you are not using Wi-Fi, you have to connect via Ethernet to your Internet router.

Please be advised the differences between phone cord and ethernet cables. They may look a bit similar, but they have very different properties. The Apple TV will certainly need an ethernet cable for the wired option; not a phone cord.

Apple TV can use wired ethernet networking, or wireless Wi-Fi networking, whichever you choose. If you plug anything in the ethernet port on Apple TV, then the Wi-Fi option is de-activated.