Is the other content you see on the screen coming from your Samsung TV, or your Apple TV set top box. That is how you would determine the source of the Picture in Picture feature you are seeing and where you would have to turn if off.
The Apple TV set top box supports PIP, but the other content of the screen would be content from your Apple TV. The options for changing that are available here:
Control video playback on Apple TV 4K - Apple Support
I don't believe DirecTV Stream initiates PIP itself, but your Samsung TV most certainly does and would be able to display both it's own Samsung TV content or that of DirecTV on the main screen, while showing a PIP window of the Apple TV content in any corner. If that is what you are seeing then turning off PIP on your Samsung TV depends on the model and that feature may also be mapped to the DirecTV remote control if that is what you are using..