Both. Substituents are a more general class of molecules, and in organic chemistry, it "substitutes" the hydrogens of a fully unsaturated hydrocarbon (
would be a completely unsubstituted molecule). Functional groups are a group of atoms associated with a specific reactivity with the compound. Thus halides can be both a functional group and a substituent as the halide connected to the carbon atom makes that carbon delta positive and more likely involved in nucleophilic attack.
However, when naming halides in organic compounds they are treated as substituents. This is what I did in class.