The distinction is relatively easy to make the Monster, in this case, is simply alive. The qualification for "undead" is deceptively simple: something that would be recognized as dead using the best techniques available to science but is somehow still moving about of it's own accord. Frankenstein's Monster, in the course of the classic story, presents us with plenty of information to determine he is alive. For example, he has to eat and thus we know that he has a metabolism since this doesn't cause him to fill with rapidly rotting food products. He can move under his own power. Brain activity is directly shown because the monster demonstrably is able to observe and intelligently interact with the world around him. We can further assume that vital functions related to these things also work. Were a medical doctor to examine him, the conclusion wouldn't be that he is undead but rather that a mass of mismatched body parts is somehow, inexplicably, alive.
To use an example, a Vampire is generally considered undead because, were you to examine them clinically, it would be fair to assume you were looking at a corpse. The mythology gets a fair bit complex since there are so many versions of vampires these days but, in general, you wouldn't expect a vampire's heart to beat, they would have no need to breathe, and lacking anything resembling a metabolism, would approach room temperature. The only thing that contradicts the conclusion that they are dead is that they can move about and interact with the world. Thus where the word came from: they are clearly both dead and not dead simultaneously.
Basically, the difference comes down to a simple distinction: something that is undead inherently relies upon some process utterly unknown to any branch of science to allow motion and (possibly) thought independently of the biological structures of the body. Frankenstein's monster is a collection of biological structures of various bodies that are functioning together to produce a living being. To put it simply, were you to take a living person and swap their heart and a lung and their liver and their marrow and anything else that can be swapped out examples from other sources and then ambulated a few limbs and replaced them with the best prosthetic money and science can buy (you monster), you wouldn't consider the result to be undead. Unlucky perhaps but such a person would be the product of a miracle only slightly less impressive than the one responsible for Frankenstein's Monster.