I don’t see what you are talking about the end shots of the casket - the close up with the hands and the long shot have the same profile.
And in the long shot in the corner of the casket (where lid meets the box)there is a triangle shape of white. it is in the same location as the “tier” in the other shot. It doesn’t show up in the close up because it is out of the frame to the left.
What you’re seeing in the corner of the casket in the photo in the front of the church at the visitation is the metal lid brace. It only goes a short ways out from the lid. The higher part on the”headboard edge” in the Diocese image goes about halfway across the “headboard” and creates a square corner in the profile.