Color Calibration vs Color Mixer
At a very high level, the key difference between the Color Calibration saturation sliders and the Color Mixer saturation sliders has to do with where they're applied. The easiest analogy I can provide is to compare how you edit a photo. Typically, you'd make one of two types of edits: global and local edits. Global edits are applied throughout your entire image, and local edits are made to a specific region using a selection tool or mask. That same principle can be applied to these two color panels.
When you use the Color Calibration sliders, you're adjusting the respective primary color in every pixel within your photo (i.e., global). Because every pixel contains a combination of red, green, and blue, the resulting edits can be dramatic.
Conversely, the Color Mixer sliders only affect the color area where the respective color is perceived (i.e., local).