That’s what they did at the bike shop.(string method with me on it) To check it I got it going a steady speed and waited for them to both settleYou can easily measure your own wheel circumference. Position the valve stem or other marking on the tire on your floor and park the spot with a piece of chalk or tape. Roll the bike forward one revolution and mark the floor again. Measure the distance between your two marks.
I would expect some random variation in instantaneous speed measurements between two different devices because they are using two different methods to measure instantaneous speed. One is doing it mechanically and the other is doing it via GPS positioning data. And how the two computers smooth out or average out data variations is going to be different. But the distance measurement over say a 10k ride should be very close to each other if the specialized is properly calibrated. If one computer says you rode 11.2 km and the other says you rode 10.3 km then you have an issue