The definition of the BSDF (bidirectional scattering distribution function) is not well standardized.
The term was probably introduced in 1980 by Bartell, Dereniak, and Wolfe.
[1] Most often it is used to name the general mathematical function which describes the way in which the light is scattered by a surface.
However, in practice, this phenomenon is usually split into the reflected and transmitted components, which are then treated separately as BRDF (bidirectional reflectance distribution function) and BTDF (bidirectional transmittance distribution function).