A modem does not 'care' about networking as it strictly a physical layer device.
As the name suggests, a modem's job is to (de)modulate signals so that they may be transmitted across various media.
Here are four scenarios in which two parties may wish to transfer data. In each case they will require a different type of modem.
Your home router connects to an ISP's access network by using a digital xDSL modem to establish a connection over a twisted pair of Copper cables (your telephone line). Some providers do this over a coaxial cable ( your cable TV line) instead. Older systems typically used analogue 56Kbps dial-up modems. If you are lucky enough to have fibre-to-the-door then you'll be given an optical modem instead.
Your mobile device connects to a wireless router using a wireless modem. This allows a connection to be established using radio waves. Similarly Infra red devices will use an infra red modem.
You are underwater and want to communicate with another vessel. To do this you will transmit data via an acoustic modem.
When you switch your mobile telephone on, it will attempt to connect to a base station (cell tower) using a GSM modem.
The point is there are many different types of modem (satellite-, voice-, soft-, the list goes on), but they all essentially do the same job.
Regarding point 2 in your post. Just because a signal is transmited over a particular (possibly exotic) medium, this does not automatically mean that the signal is analogue.
Regarding point 3 in your post. After leaving your home computer network, your data enters your ISP's access network. The job of the access network is to get your data to your ISP's core network as quickly as possible. Your data will traverse the core network and then exit "out the other side" down another access network until the it reaches it's destination.
The whole thing is analogous to the road network.