Related, but not the same.
In surface chemistry, an interface refers to the boundary that exists between one phase and another.
For example, a solid surface of a substance in air is a solid/gas interface. The surface of a piece of metal in water is a solid/liquid interface. And if you have two immiscible liquids (e.g. oil and water) then the boundary between them (the surface of the "blob" of oil, if you like...) is a "liquid/liquid interface".
Adsorption is the adhesion of chemical species (atoms, ions or molecules) to an interface with the result of an increased concentration of that species at the interface. It is distinct from "absorption" which relates to permeation through a medium.
The susbtance that adheres to the interface is known as the "adsorbate", whilst the interface is known as the "adsorbent".
The reason that "interface" and "adsorbent" are not the same is that "adsorbent" only relates to an interface when you are referring to it in the context of adsorption. Interfaces do not have to have anything adsorbed to them in order to exist,