chemical force: think about it in a terms of "chemical species" force. as for partial pressure in a mix of gazes, you can see the global pressure (like surrounding air) and the specific distribution of different species in the same volume.

yes osmotic pressure is a very important force in the circulation of ions AND water through membrane. maybe life itself (survey of one cell like for unicellular) rely on this mechanism. disturb the membrane integrity (with detegents like soap, reagents like alcohol, and specific drugs binding ions transporters like botulin toxin) and you kill the cell. so the cell life requests a very fine tuning of inside ions concentrations to maintain proper osmotic pressure inside (and so the water concentration itself) and this mechanism requires itself some energy (to be used by active ion membrane carrier). not only for nerve cells, but any cell in the organism.

hope it helps !

edit : life is a complex system. our actual knowledge must be take with humility and scientific explanations TENDS to describe it with a lot of accuracy. dont mind on your teacher for such simplification. it is a way to teach, not a way to lie. I have learnt in very different ways what could be a "protein" all along school classes but only in university I ultimately learn what was behind. and all past lessons looks "fantasy" to me now. dont be afraid to learn new things with baby steps !