The cell phone exchanges data with the cell tower. The cell tower acts as a gateway to the phone network. This channel has to carry Internet traffic and voice/text traffic. At what point does the Internet traffic get split off and a router comes into play? Does the cell tower have a connection to the Internet, or is it farther downstream?
Depends on the protocol, LTE is purely based on IP and hits a “router” at the tower and even older protocols tend to be packet based so they all hit “a router” at the tower these days but it is not the public Internet and older protocols are not IP based.
Internet traffic will be “routed” to an external gateway at an internet exchange point but the traffic for the public internet may or may not be backhauled over specific links depending on the providers network design.
The “cell” in cellphone basically means that it is “routed” BTW, just not necessarily using the IP protocol.