When editing a part's Play Mode there is a Volume parameter and a Gain parameter. I think I understand the general difference between gain and volume, but please elaborate or correct me if I'm wrong. Gain can be thought of as the input level and volume can be thought of as the output level. But I'd like to understand why is there both Volume and Gain for a part and not just one or the other?

Welcome to Yamaha Synth and thanks for the question.

Let's use factory Performance A02 "75Rd MW" as an example, you are actually recalling three Parts.
Main = 75Rd I (active)
Layer = Soft Pad 2 (inactive)
Split = FingerBa 2 (inactive)

Within the Performance these "Parts" are like three instruments plugged into three channels on a mixer. The VOLUME control is the channel fader on this "mixer".
The GAIN is the level control on the instrument itself.

If you plugged a real electric piano into channel 1 of a mixer, the Rhodes has its own volume control... (GAIN), separate from the mixer's VOLUME fader - used to balance the level with the other channels of the mixer.

It is exactly the same in the CP4 Stage.

How you can use this in a practical application... Once you understand that VOLUME is controlled by the front panel PART Control Slider, and is responsible for "balancing" the levels of the combined Parts. Then you can see how the GAIN setting can be used to set a maximum loudness for a particular PART within a Performance.

The MAIN (75Rd I) is set GAIN = 120, VOLUME = 127
The LAYER (Soft Pad 2) is set GAIN = 105, VOLUME = 61

You can see this by:
Press [EDIT]
Select 02: PART > [ENTER]
Select 01: PLAY MODE > [ENTER]
Select: Volume, Pan and Gain

Use the [PART SELECT] + [LAYER] to move quickly to the same screen on the Layer Part

So when you bring in the LAYER PART (by pressing the [LAYER] button) the programmer has set a maximum output for the Soft Pad... When you raise the Control Slider that controls the VOLUME parameter to the top, the Pad will never equal the output level of the Rhodes. This useful in live performing and when recording.

Try it - press [LAYER]
As you raise the fader of the Layer Part towards maximum (127), the GAIN setting (of 105) ensures the Soft Pad will not dominate the Rhodes sound.

You use the VOLUME to mix "live" to balance the combination of PARTs - you use the GAIN to limit the maximum output of any particular PART.

Hope that helps!