Both Cyclometer and my bike computers are set to count time while actually cycling, rather than stopped time. As John V stated, Cyclemeter reports riding time (while you are actually moving) and stopped time. My bike computers are set to only record time while my bikes are moving -- so the timer quits when you are at red lights, coffee shops breaks, etc.
Obviously, the two systems are using a different means to record moving time. However, I suspect that the bike computers are more accurate than Cyclometer. I watch the timer function on bike computers while I am riding and see them stop recording at red lights, although sometimes a few seconds might tick off before stopping. I can't actually watch Cyclometer while riding, but when I compare times after rides, Cyclometer records less time -- ranging from a few minutes on shorter rides to 5-10-20 minutes on longer rides. I presume that Cyclometer is set to stop recording time when you speed drops below a certain mph, but not sure if that's the case.
I have tried other cycling apps such as Strava and MapMyRide, but prefer the functionality of Cyclemeter. However, perhaps I should try some of these other apps to see if I get the discrepancies in time compared by my bike computers.