Brunauer–Emmett–Teller (BET) surface area is measured by specific surface area of the adsorbent. BET surface area is measured by using non-corrosive gases like $\ce{N2}$, $\ce{CO2}$, $\ce{Ar}$ etc. BET surface area depends on size and number of gas molecules adsorbed. Langmuir surface area depends on adsorption capacity of the adsorbent.
Why is Langmuir surface area always higher than BET 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.
As correctly identified, the Langmuir model assumes a monolayer of adsorbed molecules. The adsorption cross section of an adsorbate depends on numerous factors, not just the molecular size. Furthermore, the observed specific surface area is scale variant, similar to the length of a coastline. A phenomenon known as fractality. That mean that the measured surface area depends on the size of the adsorbate molecule.
