YouTube and YouTube TV don't share much other than the name, but that might change soon. Buried deep in the YouTube app is your watch history from YouTube TV. This suggests there will be some connection later, but right now it just throws up errors when you try to open a video.
There have actually been a few links between YouTube and YouTube TV deep in the settings previously, but this is much more obvious. To check it out, head to the library tab in YouTube and tap on "History." In addition to videos you've watched on YouTube, you should see live channels and individual programs you've watched on YouTube TV (you have to be a subscriber, of course). Each entry has a screen cap, watch progress, and a "Live" tag if it's a channel.
Unfortunately, none of the YouTube TV listings in your history load in YouTube. They all just produce a video page that says "This video is not available." Perhaps in the future, YouTube TV subscribers will be able to access content in their YouTube history. The fact these items show up right now indicates something is afoot.