Are you comparing 2G signal strength to 2G signal strength? Or is one of them reading 3G/4G? Or is one of them reading signal quality?
The only device you should believe is the calibrated one in the lab that's reading the signal strength with a fixed signal being fed into the phone by a calibrated signal generator. Apps and readings on the phone are to give you an approximate idea of how the phone is performing relative to past performance of that same phone, using the same measurement method (IOW the same app or the same screen on the phone). I wouldn't even bet on the impedance of the phone's antenna, which changes the perceived signal strength, and varies greatly with surrounding objects (including your hands).