Tethering on an iPhone acts as a simple pass-through of its cellular internet connection over Wi-Fi.

It does not establish a private local area network (LAN) for connected devices to communicate with each other.

The travel router can use an iPhone for internet via tethering, though that iPhone won’t also be able to connect to the network created by the travel router.

The travel router is ~the same as a home WiFi router, but they come with configurations meant for dealing with common issues on the road.