osmotic pressure vs diffusion

FysicsPhorums

I'm reading about osmosis, and the textbook I'm reading states "osmosis of water is not diffusion of water: osmosis occurs because of a pressure difference" and then goes on to state that osmotic pressure is the driving force of osmosis.

I had previously just understood osmosis to be the diffusion of water molecules (going from high concentrations of water to low concentrations of water), so I'm confused how osmosis can occur without diffusion of water? Also, although I understand that osmotic pressure can be measured by applying hydrostatic pressure to stop osmosis from occurring, I'm still not making the connection between pressure differences and solute concentrations.

Could someone help explain how osmosis is driven by osmotic pressure and not diffusion?

edit: I read in my textbook that the rate of osmosis follows Poiseuille's law, meaning it is proportional to r^4 (radius of the tube), whereas diffusion would be proportional to r^2. I think this justifies that it is due to pressure differences, but I'm still not clear on how those pressure differences arose from different solute concentrations.

PS. I tried reading the hyperphysics page on osmotic pressure, and it calls osmosis a "selective diffusion process driven by internal energy of the solvent molecules". I think this supports my original view, but I'm not sure...