Macarita:
1. Essentially all modems made in the last 5-8 years are also faxes. That includes the one in your G4.
2. When you get down to it, all faxes, including paper faxes, are just scanner/printers attached to a modem. In either mode, the modem is sending sounds to represent digitized information.
3. Fax software for your computer accepts a document, digitizes it into a grid of black and white dots, and sends that information over the modem to a fax on the other end. Essentially, it does in software what your paper fax does with a custom chip.
4. When you send or receive a fax with your computer, you're using the phone line, just as you would when you use the modem to dial in to an Internet Service Provider.
Bear in mind that when you use the fax to send or be ready to receive, the phone line is use, so you can't (a) dial in to your ISP, or (b) make or receive phone calls.
5. All fax software that I know of has a one-time price. After that, you can send or receive as many faxes as you like. That includes Cocoa eFax's $10 price.
Finally:
The use of 1 versus 2 phone lines is completely separate from whether you use a paper fax or your computer fax/modem.
If all you want is to stop using the extra phone line, and you already have a paper fax, just plug the fax into your regular phone line! Many faxes will auto-sense whether a person or a fax is calling them, and only turn on if the incoming call is a fax.
If you want to send faxes without bothering to print your documents first, then pick up some fax software. Likewise, if you want to keep a digital copy of every fax you receive, then fax software is a good idea. You can use this with a separate phone line, or your regular phone line.