Home video copies came from low-contrast 35mm interpositives, I think they were sometimes intended for video. The technology got better over time, and the transfers and mastering did too. Early transfers looked awful, some may have come from 16mm, but by the time Star Wars hit video 35mm was definitely in full use for most home video transfers.

Telecasts of 16mm would look inferior. Could be grainy, dirty, washed out, blown out, fuzzy, smearing/frame blending, even if the print was fresh there were still limitations to it being 16mm, and to the often inferior equipment used by TV broadcasters. Star Wars definitely looked inferior on ITV, I only have an AVI encode but I can still tell that the image problems are down to the actual broadcast and not the recording or capture. It may not have been overly brightened like the home video versions, but it had color casts in some scenes due to poor balance in the transfer, it could look too bright or too dark, it had that film chain look to it. (I am not sure if ITV ran their prints live every time a movie was sent out over the network, or transferred them to tape once. And I do know that when a network like ABC in America showed a unique transfer that wasn’t the home video version, like for an extended cut, even if it came from 35mm the transfer looked worse than the home video releases. There was an attempt here to IVTC the Star Trek II extended cut but the individual video fields still had blending between adjacent frames of film.)