Warm 1, 2, are usually separate from vivid/dynamic/etc, it's all personal preference and every TV has a different setting for each (though temperature might be similar across brands.)

If you get your display professionally calibrated, the tech will more than likely go into a support menu that's not readily accessible. Something like multiple buttons on the remote at the same time while also pressing other buttons on the display itself. Once in that menu they'll use whatever setting (Warm1 or Warm2, etc.) and start from scratch there so that the setting is now your "calibrated" setting.

While warm 1, 2 might be a different colour temperature across the board, the vivid/cinema options are more like Beats-style headphones in that they're not meant to be neutral but rather a different stylized version of the image.

A calibrated display attempts to reproduce colours in the most accurate way possible and would be the "correct" way to see the image. Again, that doesn't mean you would find the image more pleasing,.