only one letter different, but a big difference in technology! These processes play a central role in catalysis and gas purification - briefly explained here.
Adsorption refers to a surface process such as the adhesion of molecules to a suitable surface chemistry. Examples are:

• Oxygen “sticks” to palladium to deplete O2 in gas streams: O2 + Pd -> PdO
• Carbonic acid purification of COS using activated carbon. The process is often reversible, i.e. by heating or applying a vacuum the adsorbate “beads” out again.

Absorbing means a process for the entire volume, like a sponge absorbing water. The capacities are always larger here. Well-known examples are:

• Gas drying with zeolites: H2O + zeolite -> H2O bound in pores
• Remove sulfur smell from natural gas: H2S + ZnO -> ZnS + H2O
• capture radioactive iodine from nuclear reactors: 2 CH3I + 2 Ag -> 2 AgI + CH3-CH3
• rusting of steel

How often, when you know details about a topic, the confusion is immediately resolved!