Like caam1 says - the DVR records the actual, complete digital stream from the satellite.
When you watch playback, you are watching at exactly the same quality as live - you're watching the same digital stream of information.
That's not quite what caam1 said! Just to clarify a little more, the DVR does
not record the "complete digital stream from the satellite", nor even the complete stream from a single transponder. Rather, it records the transport stream from a
single channel (demultiplexed and usually decrypted from the
complete stream from a
single transponder), and adds a few more bytes from the previously-stored program guide in ancillary files associated with that program. I imagine that's what Cold Irons
meant to say.
Bottom line: you're watching the same decompressed and converted (D to A) digital data in all it's pristine perfection, and not a converted (A to D), compressed, and reconverted (D to A) version a la Tivo. I don't own a Tivo, but I suspect it has knobs to turn for aggressiveness of the compression, if not the two converter steps as well. A Dish network receiver has at most the scaler/deinterlacer (D to A conversion step) knob to turn on HD receivers. SD receivers of course have no knobs. If you are comparing the picture on the same TV, set up the same way, with the same cabling, and the same receiver set up the same way, then the two pictures (recorded and live)
should be identical.
All clear now?