this because my flat screen HD TV displays the signal type coming from a channel momentarily when it's turned on. I seem to remember reading that all cable and satellite HD signals are "i" (interlaced) rather than "p" (progressive) scan, but that may no longer be true.

Picture quality from a 1080i signal will be the same regardless of whether it's source is cable or satellite, unless of course the signal has digital noise, which causes blocky artifacts in the picture. However, most cable and satellite signals are pretty clean when it comes to digital noise.

As far as picture quality goes, 1080p >1080i>720p>720i. This is why the picture from blu-ray discs, which are 1080p, look so good.