Consider kerosene instead of coal to simplify the question, and more easily understand the difference between HHV and LHV.
In the USA, 1-K and 2-K kerosene grades are defined by ASTM D3699-90, and are identical except that 2-K has a higher sulfur content (0.30% max, by weight) while 1-K can have no more than 0.04% sulfur. In practice, due to stricter environmental standards evolving over time, 1-K kerosene sulfur content is typically no more than 15 ppm (0.0015% by weight) in many jurisdictions.
Both grades have identical distillation temperature profiles, and thus the same heat of combustion specifications. This is why it is a "simpler" fuel than coal, which has different heating values depending upon the type (lignite, bituminous, anthracite, etc), wide variations in sulfur content and other constituents, and more pronounced aging effects (freshly mined coal has a higher hydrogen content).
2-K kerosene can only be burned in flue-connected appliances which vent combustion gases including the water vapor resulting from combustion outside of a dwelling, and here the LHV (43.1 MJ/kg) is used. The sulfur content in 1-K kerosene is low enough that it can be burned in unvented appliances where combustion byproducts and water vapor are released to ambient air, and the HHV value (46.2 MJ/kg) is used.
The main difference between the two is the HHV value includes energy recovered by the phase change from combustion-produced water vapor to it's liquid form.
https://en.wikipedia.org/wiki/Heat_of_combustion
You'll want to do further research on how this applies to coal.