I know that regarding temperature, bond strength and energy, it is possible to make decision that the mechanism is absorption or adsorption. However I would like to be aware that in the sense of which other methods (either experimental or theoretical) I can make a distinguish between absorption and adsorption?
I dont think I understood your question very well, yet after absorption you dont have two component as they were before (i.e. when light is being absorbed with a dark plate) or lets say absorbed component go through the bulk of absorbent. but in case of adsorption it's just all about sticking of something on another one (i.e. adsorption of a surfactant on a surface)
generally you dont need to distinguish between these two as they are practically far away from each other.....
Depending on the compound, solid state vibrational spectroscopy (FTIR/Raman) can give you an answer.
on a first look both determined by name are different - adsorption onto a surface and absorption into a material. As mostly there is an intercept, when the material is not a homogeneous body, e.g. a textile like cotton fibre, which can be considered having outer and inner surface.
As long as materials are homogeneous, e.g. water/oil, you can determine concentration of ad-/absorbing compound in water and in oil to know adsorbed and absorbed amount.