The only real difference is adsorption is molecules binding to the surface of an object, in this case, activated charcoal. Absorption is molecules permeating and/or being completely broken down by an object.
Either one has a limit of ad/ab-sorption where the ad/ab-sorber becomes ineffective.
Sillica gel is an adsorbant that can be 'recharged' with heat in a moisture free area
I do not believe activated charcoal has any method of 'recharge'

