Chain lube is more like gear oil (high sulphur content and works under high pressures), but with more addititves in it to break down mud, and less anti foaming additives.
Suspension fluid is designed to have the a consistent viscocity over a range of low ish temperatures (and presumably is as newtonian* as possible in other respects as well) with very low friction characterisitcs, and anti foaming.
*newtionian describes an idealised fluid which is incompressible, neither shear thickening or thinning, constant viscocity and none of its properties vary with time, i.e. it doesn't exist, but 99% of stuff can be assumed to be newtonian.