As per above, gain is the amplification provided by a circuit. The circuit gain is changed by altering the circuit itself eg changing resistor values, feedback, removing/adding an entire amplification stage etc. So you are right, different gain settings are likely to sound different because of this.
The 'volume' control is generally positioned at the input of the preamp stage and attenuates the input signal applied to preamp's gain stage/s (from phono or line sources). There are various methods of building 'volume' controls and these will sound different. The setting of the volume control can also load the circuit differently causing changes in high frequency rolloff etc. So different 'volume' positions can change the sound.
So IMO you're right, both volume position and gain setting will change the sound. Which gain setting and which position of the 'volume' control is preferable will depend on the design, the system and likely the listener.
The 'volume' control is generally positioned at the input of the preamp stage and attenuates the input signal applied to preamp's gain stage/s (from phono or line sources). There are various methods of building 'volume' controls and these will sound different. The setting of the volume control can also load the circuit differently causing changes in high frequency rolloff etc. So different 'volume' positions can change the sound.
So IMO you're right, both volume position and gain setting will change the sound. Which gain setting and which position of the 'volume' control is preferable will depend on the design, the system and likely the listener.