I see no difference between the two,both say that degree of adsorption reaches a limiting value at high pressures and at very low pressures degree of adsorption is directly propotional to pressure. Where does the difference lie?
There is a fundamental difference between both models.
Langmuir's model was a theoretical construct, while the Freundlich isotherm is empirical.
In the Langmuir model, it is assumed that at maximum coverage, there is only a monomolecular layer on the surface. This means that there is no stacking of adsorbed molecules. The Freundlich isotherm does not have this restriction.
Freundlich gives you the amount absorbed per unit mass of absorbate, and has this absorbtion fraction be the nth root of the pressure, with n being a material-specific constnat. Langmiur gives the surface coverage, so it only allows the surface of a material to be used for sorption. Also, the functional relationship is not a root, but an inverse of the pressure multiplied by the pressure.
Qualitatively, in the limits, both seem similar, but they differ in their details and will give different answers.
The difference is that cation exchange reactions involving clay minerals are analogous to the Langmuir isotherm because the concentration of cations adsorbed can never be greater than the cation exchange capacity of the solid.