One thing that might be happening is this. Unless you use headphones with good external noise reduction or your monitors are loud enough to completely drown out the acoustic sound a guitar, even a solid body, makes when played then when you are playing you hear a mix of the amplified guitar and the acoustic sound.
 
On playback you only hear the (recorded) amplified sound, which will be different to the combination (acoustic) guitar+monitors. With my guitars at least, the tracked sound is generally a bit less bright and a bit less open than what I hear when playing with monitors/amp at low volumes.
 
If you're using an amp emulator (or an amp at low volumes) how you set the tone control(s) might also be affected by what you hear of the guitar acoustically, and when that acoustic sound is missing things are no longer set correctly to give the sound you want.

Follow up. I did the test and did find my problem. I had the Input Gain of the track at a non zero value. The Input Gain control is bypassed during record/monitoring but (of course) not in playback.
 
As the official signal flow chart clearly shows, it is a feature not a bug but something critical to pay attention if you use amp simulation with effects sensible to input volume (like compressors): 
 
Thanks to all for your answers.

Thanks for following up with the forum to let us know. Glad you got it figured out.