Does Modem Have An Integrated Routing Feature

What I am trying to do is port forward certain ports so the servers I'm trying to run will allow other people to connect.So far I got no where since I got a new ISP. They can't provide any assistance since I use a netgear router. One of their tech support said their modem has a built in router. The rest all said no. I noticed that the IP in CMD when I type ipconfig /all is 192.168.1.(15-47) it switches every now and then. But that is a local IP. Wouldn't that single that the modem is already routing the IP? When I put my router on it switches to 10.0.0.(2-55). These are all local IP's though. Does the modem have an integrated routing feature? Verizon really sucks so far. They can't answer their own questions without conflicting with each other.

The modem is getting the IP, and putting it into a local IP (What I believe is a routing feature) for the network. Now the local IP goes to the netgear wireless router, and gets routed again (Changed the local IP to 10.0.0.?). The netgear only got a Local IP the first time however, so the external IP is not being... worked with in the netgear router. It is trying to port forward for the local IP address, which already works for me obviously, however it is not a WAN IP address and therefore no one else is able to connect to any of my servers.And lastly, verizon states they have only "Modems" and "Wireless routers" so if they have no modems that doesn't come with this feature, then I need to learn how to port forward while the IP is being routed twice, similarly to when you have two routers hooked into each other.