When does DIFFUSION occur and not OSMOSIS, and the otherwise?
But when does exactly osmosis occurs instead of diffusion?


These processes are not mutually exclusive. Both can happen simultaneously. Their rates depend on different parameters such as permeability of the membrane towards water and the solutes. A semi-permeable membrane has different permeability for different molecules. There are cases when one of these two processes may happen but not the other (again, a function of the parameters):

Osmosis+/Diffusion- 
When there are no solute transporters expressed in the membrane of the concerned cell. For e.g. RBCs do not express the Sodium-Chloride symporter. It is expressed in the distal convoluted tubule of the nephron.

Osmosis-/Diffusion+ 
When the osmolarity of the cytosol is same as that of the ECF and the cell expresses ion channels. The action potential in a neuron would be an example of this phenomenon.