Rather than computer screens adjusting to different websites, individual websites respond differently to either the size of the screen or the size of the browser window. Websites that can adjust their formats based on screen or window size use a web design approach called responsive web design.
A computer screen, or more accurately, its resolution (the measure of the dimensions of a display in terms of pixels, or individual color-producing dots), does not adjust to different websites because this setting is controlled by the operating system. Browsers are programmed to leave these settings alone for security reasons.
To allow content to display properly on different screens, websites are often programmed to adjust dynamically to the size of the browser window they are displayed in. This is done by telling the browser to display different elements at certain percentages of the window's height or width.