Henrys law is a limiting law that only applies for "sufficiently dilute" solutions, while Raoults law is generally valid when the liquid phase is almost pure or for mixtures of similar substances. The range of concentrations in which Henry's law applies becomes narrower the more the system diverges from ideal behavior. Roughly speaking, that is the more chemically "different" the solute is from the solvent.
For a dilute solution, the concentration of the solute is approximately proportional to its mole fraction x, and Henry's law can be written as
This can be compared with Raoult's law:
where p* is the vapor pressure of the pure component.
At first sight, Raoults law appears to be a special case of Henrys law, where H = p*. This is true for pairs of closely related substances, such as benzene and toluene, which obey Raoult's law over the entire composition range: such mixtures are called ideal mixtures.
The general case is that both laws are limit laws, and they apply at opposite ends of the composition range. The vapor pressure of the component in large excess, such as the solvent for a dilute solution, is proportional to its mole fraction, and the constant of proportionality is the vapor pressure of the pure substance (Raoults law). The vapor pressure of the solute is also proportional to the solutes mole fraction, but the constant of proportionality is different and must be determined experimentally (Henry's law). In mathematical terms:
:Raoult's law: 
:Henry's law: 
Raoult's law can also be related to non-gas solutes.