Like most everything, diffusion (along with related phenomena like mixing) is governed by thermodynamics. In an ideal solution, the responsible party is basically entropy. Indeed, in the first scenario the glucose will spontaneously diffuse through the membrane into the other chamber until the concentrations on both sides are equal - the rate of forward diffusion is balanced by the rate of backward diffusion. This would happen in the second scenario as well except there are other forces at work. As chloride diffused, this would result in a gradually increasing positive charge in the original chamber, and a gradually increasing negative charge in the other one. Separating charges requires energy, quite a bit, in fact, and therefore this diffusion would not be a spontaneous process. We could envision making it happen by applying an electric bias, but even then you'd quickly reach a point where the energy cost is too great for further charges to move effectively. (This is, by the way, essentially why a salt bridge is required in an electrochemical cell.)
In a filtration, gravity is a force of bias (slowing down the rate of backward reaction), to drive the equilibrium point forward. But gravity would likely not be enough of a forward bias to overcome the negative electrostatic force that would accompany the separation of charges occurring if chloride only passed through your filter.
This all presumes the hypothetical chloride-only filter could be created in the first place.