Adsorption - the adhesion in an extremely thin layer of molecules (as of gases, solutes, or liquids) to the surfaces of solid bodies or liquids with which they are in contact. Adsorbance is the addition of a molecule to a surface of a molecule.
Absorption - to suck up or take up (a sponge absorbs water). In the case of absorbance, the molecule being absorbed is taken up into the internal network of the absorbing material. Absorbed water molecules are not easily evaporated.