Interesting question. Speaking as a controller I thought they were the same thing. Can you give an example where both are available on the same beacon - maybe looking at the plates will give a hint?
I've always thought that the difference between an NDB and LOC was that the former was certified and flight checked as both an en-route aid and a let-down aid (i.e. does it give a good signal close to the ground) whilst the latter was only checked for en-route nav.