The key difference in video quality between a 1080p YouTube video and running a game at 1080p on your monitor lies in the way the video is compressed and delivered.
When you watch a 1080p video on YouTube, the video has gone through significant compression to reduce the file size and allow for efficient streaming. YouTube uses lossy video compression codecs, which means that some visual information is discarded during the compression process. This compression can result in a noticeable loss in image quality, especially in scenes with a lot of motion or detail. The amount of compression and the resulting quality can vary depending on the video's bitrate and the algorithm used by YouTube.
In contrast, when you run a game at 1080p on your monitor, the game is rendering the image directly on your hardware without the need for significant compression. The game engine is able to deliver the full 1080p resolution without the same quality loss as a compressed YouTube video. This can result in a sharper, more detailed image, with fewer compression artifacts and better overall visual fidelity.