Answer
The reason why HOS logs do not exactly match the Trips History is because the trips are recorded based on a different logic for HOS logs.
For HOS to record a Drive Log, the vehicle needs to travel at speed greater than 5miles/hr (8km/hr). However, Trips history will include all vehicles movements regardless of the speed.
It is also important to look at device unplug events. Device unplug can mess up trip history and HOS logs.