The professional video tape decks had separate read/write heads. The digital formats could do a pre-read by having the playback head in front of the record head. The signal could then be routed through whatever equipment in the studio to do whatever one needed and then recorded back to itself with the updated video. This was only allowed on a source with a CLONE sticker to guarantee the ORIGINAL was not being updated this way.

Been a long time since I've dealt with audio gear, but I'm pretty sure they also had separate playback/record heads in the tape path as well.