Im just studying about this topic as well
so I think the difference is that Bingham is one of rheological model and a time independent behavior for low MW polymers where as pseudoplastic is one of power-law behavior where n<1 or it also known as shear rate thinning since viscosity decreases with increase in shear rate. So both of them are just two different models I guess although they have the same behavior in the case of viscosity and shear rate. Hope this helps. Cheers