The difference between the Saturation and Vibrance sliders in Lightroom Classic is that the Saturation slider makes absolute adjustments that affects all colors equally. Moving the slider to -100 will remove all saturation from an image (making it appear monochrome), where as moving the slider to +100 will fully saturate the colors in an image.
The Vibrance slider is relative. Moving the slider towards -100 decreases the amount of saturation relative to how much saturation there was in the color to begin with. Moving the slider towards +100 increases the relative amount of saturation while trying to avoid pushing saturated colors to full saturation (to help minimize clipping colors to the same value as they approach full saturation). The Vibrance slider is also biased: it adjusts orange, red, and yellow values less than other colors. This can be helpful when trying to increase saturation in a blue sky and green grass in an image for example, while avoiding shifting skin-tones, preventing them from becoming over saturated.
You can use the Saturation and Vibrance sliders in combination with one another. Below I’ve set Saturation -50 to lower the overall saturation of the colors, and then set the Vibrance to +100 to increase saturation in the non skin-tone colors (magenta, purple, blue, aqua, and green).
While these illustrations demonstrate increasing/decreasing Saturation and Vibrance using a gradient, I would encourage you to experiment with the sliders on your own images to get a better feel for how they will adjust the colors in you photographs.
When using the Quick Develop panel in the Library module, press Option (Mac) | Alt (Win) to toggle the Vibrance to Saturation. See this post (The Power of Quick Develop) for additional information on the Quick Develop panel in Lightroom Classic.
And here are links to several additional tools in Lightroom Classic that you can use to change colors including White Balance, the HSL/Color panel, the Color Grading panel, and Masking.