Digital watches and clocks have a digital display. That is what makes them digital watches and clocks. Whether they record time in a digital or analogue fashion is irrelevant. A digital display will not point out the current time on a display of all times possible, as it does in an analogue watch, but it will only show the digits of one time. Nowadays this usually happens via LED or LCD display, but that has not always been the case. Digital watches have been around long before the electronic display was invented. They used turning disks or cylinders behind a mask that would only show one digit at a time. Or airport-style flip-card mechanics were used.