4K videos and images appear crisper than 1080p on a 1080p display because they contain more pixels, which results in a higher resolution. A 4K video has four times the number of pixels as a 1080p video, which means that it can display more detail and a higher level of clarity. When a 4K video is played on a 1080p display, the video is downscaled to fit the display's resolution, but the additional detail and clarity of the 4K video is still visible, making it appear crisper than a 1080p video.
Additionally, 4K videos tend to be encoded using high-efficiency codecs, such as HEVC, which makes them more highly compressed than the average 1080p video. While this compression does not inherently affect picture quality, it does allow for more data to be moved, resulting in a higher bitrate. This higher bitrate, combined with the increased resolution of the 4K video, contributes to the overall crispness and clarity of the image when displayed on a 1080p display.