Confusion in solubility expressions in Henry's Law While reading about Henry's law and solubility I frequently come across two relations:

$C = k_{h}P$ (c = concentration of a dissolved gas)
$P = k_{h}x$ (x = solubility/mole_fraction)

What is the difference in these two expressions, do they seem to contradict each other? I am not able to decide whether a gas with higher $k_{h}$ would be more soluble or less soluble.
Please help me out with the same I am new to this topic
Sander (Ref. 1) has compiled a useful review of Henry's law constants in water that includes an introduction showing notation and conversions.
There are two types of Henry's law constants:

Solubility constants convert from pressure to concentration in solution (solubility):

$$c=Hp$$

Volatility constants convert from concentration in solution (solubility) to pressure:

$$p=Kc$$
Usually it is possible to determine which constant is reported by inspecting the units.
References

R. Sander. Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys., 15, 4399–4981, 2015.
www.atmos-chem-phys.net/15/4399/2015/doi:10.5194/acp-15-4399-2015