BRFD / BSDF
The Bidirectional reflectance distribution function, in short BRDF, is used to determine how light is reflected off of a surface. Basically, this function is responsible for how the shading and reflections on your 3D model look like when rendered. It's a very technical topic by nature, but the important takeaway for the artist is that there are plenty of different models out there, ranging from "Phong" to "Blinn" (on the more historical end of the spectrum) over "Ward" and "Cook-Torrance" to "Beckmann" and "GGX" (the more modern ones). Many modern game engines and offline renderers use the "GGX" model for their PBR Shaders.
A BSDF or Bidirectional scattering distribution function is not quite as standardized as BRDFs are and is sometimes used in different contexts. The important thing to know about it is that it includes scattering, meaning light entering a translucent surface. It is usually not exposed to the artist and thus of little relevance for the end-user but the term is often used interchangeably with BRDFs.