The adsorption evolvement is explained by the adsorption kinetics and the dynamics of the process can be easily understood from the study of the kinetic models. The kinetic models also give the reaction order for which the reaction is happening and they define the adsorption kinetics.
Parameters such as capacity of adsorbents, expression of surface properties, adsorption mechanism pathways and effective design of adsorption are optimized using the kinetic isotherms and the isotherms are influenced by the type and nature of the system.
Read through the attached papers they will give an idea
Adsorption kinetics also controls the rate of adsorption, which determines the time required for reaching equilibrium for the adsorption process.Pseudo kinetic model in adsorption process provide an insight into the adsorption mechanism, surface properties and affinity of the adsorbent.
Akito I Sema, already you have got accurate answers. I am just adding a summed-up brief answer.
Both represents the variation of adsorption capacity (Qe), but against different parameters: equilibrium concentration of adsorbate (Ce) and time (t). In either of the cases, it encompass the region of start to saturation (i.e. rapid change of Qe up to almost no change of Qe). Now, these variations are fitted with several equations. The ultimate goal is to know the adsorption mechanism.
Akito I Sema, The main difference is that the adsorption equilibrium state can be described using isotherms, and the course of the adsorption process over time (changes in adsorbate concentration or adsorption capacity) using kinetic equations inserted into the mass balance equation. It is worth remembering that the state of equilibrium is the limit state to which the adsorption process is heading, and therefore the mass balance for dC/dt=0 (dq/dt=0) should reduce to a specific isotherm. Unfortunately, only a few studies pay attention to it, and a frequent situation is the use of, for example, the Freundlich or Langmuir isotherms to describe the equilibrium data and the so-called PFO or PSO to describe the kinetic data. There is no justification for this.
Madhukar Baburao Deshmukh, You wrote that ". Pseudo kinetic model in adsorption process provide an insight into the adsorption mechanism, surface properties and affinity of the adsorbent." Can you prove it? For the record, what you call PKM is actually either an empirical exponential function (PFO) or an empirical hyperbolic function (PSO).