The full-screen display has nothing to do with, iPad, HDMI, or your TV brand. It depends on the aspect ratio of the content and your TV. If the video is 1080p or any resolution having an aspect ratio of 16:9, you will see the content on the entire screen. But if the aspect ratio is other than 16:9, there will be black bars on the sides.
Some apps, such as Netflix, play the content according to the aspect ratio of the device. For instance, when you connect your TV to your phone using HDMI, Netflix will automatically play the video having the correct aspect ratio according to the TV.