In everyday language (in the US), these two words mean similar things. They can both be used as a noun to indicate something left behind after something else has been removed. More commonly however, residue is used as a noun, and residual is used as an adjective.
BUT, if you are talking about residue and residual in the context of a farm where animals graze -- (this is much less commonly used) -- residue refers to the dead plant material on the ground after an animal has grazed, and residual refers to the remaining alive plant material still growing.
Most US English speakers in regular (non-farming) conversation will use residue as a noun and residual as an adjective, however "residual" can also be used as a noun, and has the same meaning as residue.
Hope this helps!