How does Task Manager compute Up Time, and why doesn't it agree with GetTickCount?

Task Manager shows a piece of information called “Up time”. How is this value calculated, and why doesn’t it agree with the value reported by Get­Tick­Count/Get­Tick­Count64? Task Manager calculates “up time” by subtracting the system boot time from the current time. In other words, it is misnamed; it really should be called time since system was started. It doesn’t subtract out the time when the computer was in sleep or hibernation.

The tick count, on the other hand, counts only time that elapses while the computer is on.