A general idea we have about osmosis is that it is the movement of solvent particles through a semi permeable membrane from a region of high concentration to a region of low concentration.
You have to carefully specify which concentration you refer to. The net transport is from regions of high solvent concentration (low solute concentration) to low solvent concentration (high solute concentration).
This seems correct in case of a gas. Gaseous particles spread through any container in which they are kept, which makes it seem to us as if they moved from high concentration to lower concentration.
It does not just seem as if, that is what actually happens as net effect. The reason that more particles move out of a region of high concentration is because there is more of them.
But in the case of a liquid how is this true? For example consider a bottle half filled with water, water never moves from high concentration to lower concentration inside the bottle.
That would be an example of a phase change. Water molecules do move from the liquid to the gas phase and vice versa. However, because the water molecules interact in the liquid and don't interact in the gas phase, most water molecules are in the liquid phase. The reason that some are in the gas phase is that they are more dispersed in that phase and mix with other components of air, both of which is entropically favored.
So is it wrong to explain osmosis as a special case of diffusion?
No, it is perfectly alright to explain osmosis with diffusion. There is a higher concentration of solvent on the side of the membrane with lower solute concentrations, so more solvent molecules move away from that side than move to that side.
What actually makes solvent particles move from regions of higher concentration to regions of lower concentration? Is it solute attraction?
No, this also works for ideal solutions, where the solute:solvent interactions are very similar to the solvent:solvent interactions. It is a process driven by entropy, not enthalpy.
Or a difference in pressure in pure solvent phase and solution phase?
In a system where the liquids have room to expand, the pressure is the same. In a system where the liquid compartments are kept at constant volume, the pressure on the side of higher solute concentration increases (because the amount of solvent in that compartment increases through osmosis). So the pressure difference is caused by the osmosis, not the other way around.
There is a process called reverse osmosis used to purify water, where the pressure differential results in water going from the "dirty" compartment to the "clean" compartment.