Featured Image - Question re- using on Pages vs. Posts

I noticed that this feature works as shown on the video for "Posts". I tried to use the feature on "Pages" and was, at first, unsuccessful. I tried several times in the Page section and was finally successful only when I avoided the default template and the full - width page template -no side bar choice.

Can I conclude that if I want a featured image on a "Page" as opposed to a "Post", I must select the Full page template for the image to appear??
I am aware that I can place images in a page using the media function.
I am really only asking about the "Featured Image" issue.
Thanks, Al Tallakson