PVR - Personal Video Recorder. PVR software allows you to record programs from cable or OTA (Off-the-Air) antenna) on your PC using an appropriate tuner.
QAM - Quadrature Amplitude Modulation. It's the transmit method used by both digital cable and FIOS (Verizon's fiber optic network) for digital TV transmissions. A PC with PVR capability can only record in-the-clear QAM channels (i.e., unencrypted). The number of clear QAM channels varies based on the provider you are using. Some providers do not offer any clear QAM channels whereas others have quite a few of them, most of which are usually restricted to local channels.
HDHomeRun - a networked ATSC (i.e., digital Hi-Def) tuner that transmits shows over your home network to a PC.
Basically, you need a PVR program and a tuner to convert any PC into a PVR. These include BeyondTV and SageTV (both commercial apps), MythTV (Linux based), GBPVR, and several others. Guide data is free with any of these apps as long as you keep the PC connected to the internet for frequent updates. There is even software available that mimics a Tivo interface, but it does require a Tivo subscription to use it.
There are numerous tuners available with various capabilities.
Here's a good source of info for HD tuners. You can have internal tuners (PCI or PCI-E interface) or external tuners (USB or network interface). You can have tuners for analog, digital, or QAM or a combination of two or more types.
You can also interface with a provider's set-top box (i.e., cable, FIOS, or satellite TV) and control the channel switching of the box using an infrared repeater of serial interface from the PC. The output of the box is connected to a video capture card or tuner card with A/V connectors. You can capture HD programs from a STB using Hauppauge's HD-PVR box using component connections.
