I have my pc connected to the iPhone hotspot. My router is connected to the pc using Connectify. I have multiple devices connected to the router. What I would like to do is replace the pc with the Raspberry. Is there an easy way to connect the router to the Raspberry while the Raspberry is connected to the iPhone data? I don’t know what term to use for the function I would be using. Maybe an access point, bridge, or host.
It is unclear how the PC is connected to the router. I assume it is connected wired with an ethernet cable. I also assume you want to use the iPhones internet connection to give all devices on your local network access to the internet. With this conditions you have to use the Raspberry Pi as additional router, instead of the PC. Its wired port (interface eth0) is connected to the already available router and with its WiFi device (interface wlan0) it is connected to the iPhones hotspot using a WiFi client connection. Now the RasPi must be configured to route the network traffic between the two interfaces eth0 and wlan0.
You can look how to use a Raspberry Pi as WiFi router. In this example just replace the words "desktop computer" (not confusing it with your PC) with your router and "WiFi internet router" (not confusing it with your already available router) with your iPhone. Then it should do.