Under what circumstances are the three color modes provided by Nikon digital camera used for shooting?

I also use Nikon. I don't know your specific model. Take D300 as an example. The camera's shooting menu page has a color space option, which defaults to sRGB. You can choose that, because AdobeRGB is a more advanced color gamut, and ordinary monitors can't display such rich colors. Even if the screen display cannot be checked by a professional screen colorimeter, color cast will occur. Therefore, it is recommended that you use the default SRGB.