Diffusion-controlled reactions, activation-controlled reactions and rate equation
To add a little to what @geo has written. In all types of bimolecular reactions in the liquid phase, the reactants diffuse together; they have to, there is no other way for them to meet. The reaction is diffusion controlled if the activation barrier is so small that the first time the reactants meet, reaction is effectively instantaneous. This means that the barrier is only a few times average thermal energy (3RT/2) and that reaction occurs before the species can diffuse apart again. 

In an activation controlled reaction the species repeatedly meet by diffusion but only occasionally$^*$ do they acquire enough energy from the surrounding solvent molecules that, at that instant, have enough energy to surmount the activation barrier.  Once they have reached  the barrier top the energy fluctuations that caused the barrier to be surmounted in the first place must cease after the transition state is crossed and products are then formed. (Recall that molecules in solution are continually jostling about and, from the Boltzmann (exponential) distribution, there is always a small chance that a molecule has, by random fluctuations, and for a short time, many times the average energy ).
$^*$By 'occasionally' I mean perhaps 1 in a million or even tens of millions of encounters.