To record TV from a cable set-top-box on your hard drive, you will need a TV tuner card that has analog input port, either svideo or composite, or both.
Most cable and satelite STB have analog video out, either svideo or composite, or both. As these signals are usually unencrypted, you can record them to your hard drive.
Just connect the STB analog out to the tuner card's video in, and use the software that came with the tuner card to record or watch. Or use Windows Media Center.
Note well that not all TV tuner cards have a separate analog in port. In other words, these tuner cards can not capture video from a video source like a STB, VCR, or camcorder. For instance, the Dvico Fusion 5 Lite does not have a functional analog in port, and therefore you can not capture video with it.
More problematic is being able to watch one TV program while recording another from a single STB. I'm not aware of any tuner card that can do this, as all of the video in and out will be controlled by the STB. For instance, I have a TiVo box for my DirecTV, and it has dual input from the satelite dish. The TiVO allows me to watch one satelite show while it records another. But, the TiVO does not have two video out ports, so I can only record one TV program on the hard drive and, therefore, it is the only TV show that I can watch live on the PC monitor.
By the way, I do not always watch DirecTV from my PC. My TiVO has a direct connection to my LCD TV, which has multiple video inputs. The PC connection to the LCD TV is via DVI.
I suppose that, if you have a cable or satelite STB with two video out ports, you can connect each to two separate TV tuner cards in a PC. With Windows Media Center, you can record simultaneously from every TV tuner that you have in your box (max. two analog tuners and two HD tuners). Accordingly, if you are able to have two separate cable TV sources, you can connect each to its own tuner, which will capture and record for you in WMCE.
As for other software other than WMCE that can do this, I don't know. My experience has only been with WMCE.
I've never used the ATI AIW cards, so I have no opinion on them. I believe that all of the AIW tuners are analog only, not HD.