In the case of the difference, both were being played in Safari. One was a URL of a Live stream played in Safari and the other is a URL of the recorded stream (of the Live show) in Safari.
Both were the same show, both in Safari (compare the last 2 images above). Only the source of the stream is different. One comes from getting the URL from “Live”, e.g. “<IP:18080>/stream/pls.m3u8?mEmWmILUi4xhCtnQpZHJJA” and the other comes from the pvr playslist of the show being recorded, e.g. “<IP:18080>/pvr/52/pl/playlist.m3u8”