Resolution is the biggest part of the picture, but don't neglect frame rate. Film masters are 24 fps, NTSC video tape 29.97 fps, material originally shot in HD 60 fps. That's why HD is so noticeable in sports or in action flics -- depending on the source and what's going on on screen, 720p at 60fps can look better than 1080p at 30 or 24 fps.
Upconverting and deinterlacing video involves a computer making its best guess at what comes between frames or between lines. It's like blowing up a picture to a higher resolution in Photoshop. A good algorithm is better than a bad one, but the best algorithm is a poor substitute for quality source material.
I recall hearing in the early days of HD broadcasting that TV Land was one of the first networks to have a substantial HD library. Network shows of the last several years were shot straight to tape, while the older shows had film to go back and scan.
Actually, for about the last 20 years there’s been very little origination of network series on video. With the exception of “live” reality shows and soap operas, most episodic series are shot on film, then transferred to tape for post production. The days of the old four-camera sitcom video trucks pretty much died out. The reason was that foreign customers stopped buying US shows because the standards converted product looked worst than their home grown stuff. The studios moved heavily into film so that they could do PAL and SECAM syndication transfers from the negative.
Starting in about ‘94, a gradually increasing percentage of the original film transfers for the US product were in HD instead of SD. We cut the shows on HD, then down-ressed for broadcast. So that’s why there’s HD masters for those shows.