What is the difference between BET and Langmuir model for calculating the specific surface area?
Langmuir adsorption model considers that only a monolayer of adsorbate can be formed on top the surface.
In contrast, BET model considers multilayer formation.

Then, if (as generally occurs) multilayers are formed, BET is able to consider that they are not being formed by directly covering the surface, but by covering extra layers. Langmuir will consider that multilayers can only form as the first adsorbed layer, thus resulting in an exaggerate (unrealistic) surface area.

You can clearly see the differences in the Wikipedia page for Langmuir adsorption.