The key difference between playing a 4K video on a 1080p monitor and watching a native 1080p video lies in the way the video is displayed.
When you play a 4K video on a 1080p monitor, the video has to be downscaled or resized to fit the 1920x1080 resolution of the 1080p display. This process, known as downscaling, means that the 4K video's higher level of detail and sharpness is reduced to match the 1080p display. While the 4K video may still appear better than a 1080p video on the 1080p monitor, it won't have the same level of detail and clarity as it would on a native 4K display. The monitor simply doesn't have enough pixels to display the full 4K resolution.
In contrast, a native 1080p video is designed to be displayed at the 1920x1080 resolution, so it will be shown at its full quality on the 1080p monitor without any downscaling or resizing. This means that the image quality, sharpness, and detail of the native 1080p video will be preserved, as the video is being displayed at its intended resolution.