Monitor drivers are specific to the monitor. They are usually text files that tell the operating system what the monitor is and what it is capable of. They are not required for the monitor to function.
Your video adapter lets your computer communicate with a monitor by sending images, text, graphics, and other information. Better video adapters provide higher-quality images on your screen, but the quality of your monitor plays a large role as well. For example, a monochrome monitor cannot display colors no matter how powerful the video adapter is.
A video driver is a file that allows your operating system to work with your video adapter. Each video adapter requires a specific video driver. When you update your video adapter, your operating system will provide a list and let you pick the appropriate video driver for it. If you do not see the video driver for your adapter in the list, contact the manufacturer of your video adapter to get the necessary video driver.