What is the (conceptual) difference between binding energy and adsorption energy?
For solids, the binding energy is what makes the crystal (if you will) hold together. It is what makes the individual constituents of the compound bind together.

Adsorption however is an entirely different process: Here, some molecules interact with the surface of another compound. Since (strictly speaking) this is no chemistry but mere physics (there is no formation or breaking of bonds) there are other interactions at play, mainly van der Waals-type interactions.

As these are weaker (it's easier to wipe off the water from your windshield than rip out a silicon atom) and aren't based on the same principles as the binding energy, they get a different name.

I hope that cleared things up for you.