If I buy a movie on YouTube, will I also own it on the Google Play Store?
Yes, movies purchased on YouTube will be in your Google Play Library and vice versa.
According to Android Authority, video purchases from the Google Play Store have been integrated with YouTube since 2014.
[...] Google has just updated its back end to integrate your Google Play movie and TV purchases into the Youtube app, bringing the service in line with the desktop feature.
You will now be able to find all of your movie and TV purchases under the new Purchases section in the Youtube menu, right under the Watch Later option.
While Android Authority doesn't specifically say whether YouTube purchases are synced to Google Play, an old Reddit thread confirms that yes, movie purchases are shared between YouTube and Google Play.
While it's true that movies bought on youtube then appear in Google Play, the two are not entirely interchangeable. Specifically, a movie bought via youtube is not viable to be added to your Google Play Family Library, should you have such a thing set up.