Standalone Tivo:
When recording analog signals ("normal" tv using internal standard broadcast tuner, or signals decoded by an external box and sent to the Tivo as analog signals) the Tivo must digitize the signal in order to record it. You choose the image quality to use when digitizing the signal. Better qualtity takes up more disk space, so it's a tradeoff according to your personal tastes, and how things look on your particlular TV setup. You can generally get away with viewing lower quality on smaller tv screens.
DirecTV Tivo:
Records the digital data stream from the satellite but does not decode it into analog until you play it back. Thus you get the identical playback quality as if you had watched it "live". No provisions for digitizing other analog signals, so no inputs for analog signals from other sources.
In BOTH cases, you generally have several options on how to hook up the output of the unit to your tv. Use the highest quality option that is supported by your tv.
RF output - internal RF modulator that synthesizes a tv channel, usually selectable as channel 3 or 4. Starts off with a composite signal (see below). Worst option to use. There will be some signal degradation of the composite signal as the signal is modulated in your unit. Also, a GOOD modulator is fairly expensive so they only put cheap ones in consumer goods. Almost assuredly monoaural sound. My DTV Tivo doesn't even have this option, don't know about standalone Tivos.
Composite output - All video information (all three colors, red, greeen, and blue) combined into one video cable, usually color coded yellow. Some degradation occurs but you don't have further degradation introduced by an RF modulator. Separate cables for video, left audio and right audio. Better than RF.
S-Video - splits the video information into two separate signals, "luminance" and "chrominance", basically brightness information and color information, via a 4-conductor cable with 4-pin connectors. Greatly reduces signal degradation compared to compositel. Video only - must use with the L and R audio cables.
Component output - three separate cables send same "luminance" info as S-Video, but splits apart the two "chrominance" signals which are combined into one in S-Video. In greatly simplifie terms, this means you're sending the red, green, and blue signals separately in a way your tv can use directly for best quality picture. (This option available in DirecTV units, don't know about standalone Tivos).
