Zwift reads directly from your sensors, whether that's a speed/cadence sensor, power meter, or smart trainer, which means that you do NOT need a bike computer. Instead, we recommend using the Zwift Mobile Link app for iOS and Android devices which performs the same functions and works as a game controller.
If you do decide to use a bike computer, however, the speed/distance on your bike computer will be different from what's shown in Zwift.
While speed sensors measure speed and distance based on your physical tire rotations, Zwift measures these based on watts, course incline, your weight, and other factors - such as whether you're drafting. Because of these different factors, it's not unusual for your speed and distance in Zwift to differ from what you're seeing on bike computers. The two will rarely, if ever, match up.