What is the difference between max-device-width and max-width for mobile web?

max-width is the width of the target display area, e.g. the browser

max-device-width is the width of the device's entire rendering area, i.e. the actual device screen

Same goes for max-height and max-device-height naturally.

max-width refers to the width of the viewport and can be used to target specific sizes or orientations in conjunction with max-height. Using multiple max-width (or min-width) conditions you could change the page styling as the browser is resized or the orientation changes on a device like an iPhone.

max-device-width refers to the viewport size of the device regardless of orientation, current scale or resizing. This will not change on a device so cannot be used to switch style sheets or CSS directives as the screen is rotated or resized.