iPhone to iPhone communication

The following distinguishes (possibly) paying for Wi-Fi access, from paying for cellular data, from paying for a cellular call.

FaceTime, Messages, Signal, or some other chat app, there are no data charges past local data access costs if any.

If you’re on a local residential or coffee shop or other Wi-Fi, there are no added costs once you are connected to the Wi-Fi. Most Wi-Fi networks either don’t charge, or charge some fee or require some purchase to connect for some specified time interval.

If you’re using cellular data for a chat app, the data used will either be part of your cellular plan, or you will have to pay for the cellular data. (But this cellular data payment is no different than browsing the web or streaming a video from some service. You either pay for that cellular data or your plan includes it. But that’s all entirely independent of where the other end of the chat app connection is located.)

Cellular calls from device to device, yes, your carrier plan must either cover international calls, or one or potentially both carriers involved in the call will charge for the cellular call.

Communication using FaceTime and iMessage is free across the globe and only the internet charges may apply if you are using Private WiFi.