The 8-bit vs 10-bit aspect is entirely unrelated to the HDR vs SDR aspect. 10-bit is just added precision in your numbers, and ought to be interpreted as addin

The 8-bit vs 10-bit aspect is entirely unrelated to the HDR vs SDR aspect. 10-bit is just added precision in your numbers, and ought to be interpreted as adding more decimal places (makes more sense when you imagine the values going from 0-1 instead of 0-255). HDR is indicated as a bit somewhere in metadata to tell the downstream components how to interpret the pixel values. To be extra pedantic, HDR is a bit to indicate how to interpret the brightness (luma) channel. There will be other bits for signaling how to interpret the color channels. Often these things are all done together, which is generally referred to as HDR10.