So I was wondering what the difference would be between raising the input or the limiter gain (with adaptive gain off). In both case the limiter works at 0 dB. So would there be a difference between using the input of limiter gain in this case?

Actually, there is a difference.  When you apply GAIN in Elevate that GAIN value gets incorporated into the machine learning algorithm as the target GAIN that your setting.  The algorithm tries to hit that target gain while also satisfying the other constraints (SPEED, ADAPTIVE GAIN, ADAPTIVE SPEED, and the auditory model).  It weighs all these values against each other and to try to hit the requested target based on the incoming audio.  The INPUT LEVEL on the other hand is just a linear input level control.  Essentially, the best idea for a loud master is to set the INPUT LEVEL controls such that your audio is just below clipping and use GAIN control to increase the level.

Dan