@shrinkrap - I agree that the episodes displayed on their own website page look much cleaner and keeps you away from all the clutter of Facebook. I’m really not too familiar with Facebook Watch as a product, but it’ll be interesting to see how the relationship between them and their publishers evolve over time.
“hosted” - it looks like they are using Facebook as the provider to store, upload and stream their video files. The player that displays the video for you on these pages is owned by Facebook; however, because Mind of a Chef has currently designated those videos as “public”, you don’t need to be a Facebook member to view the videos on their Facebook page or from anywhere else they choose to house references to that original video. If they chose to change those permissions at some point, it’s possible you may need to be a FB member to view the videos, but not for now.
“embedded” - This means that the same video they originally uploaded into Facebook can be inserted into a video player and shown from any other website (in this case, Mind of a Chef’s own website) for people to view, as in the link above.
Hope this helps to explain a few of the terms you asked about above. I’ve also included some related links that might be of interest.