Skeletons vs. Undead

I was thinking of upgrading my sword to kill some undead when i noticed there is:
Of Deathbane: Damage +1-20% (vs. Undead)
Of Skeletonslaying: Damage +1-20% (vs. Skeletons)

I always thought skeletons were considered undead. So, does that mean if i got the Deathbane upgrade, it'll have no effect on the skeletons? Secondly, what all are consider to be in which category? I assume now that i know that they all don't just belone in a Undead category, that all the ones that accually say skeleton in there name are skeletons and so are hellhounds cause they look like nothing but bone, but what about Wraiths and that sort? Are bone fiends, minions, and horror all accually considered in the skeleton category, cause isn't one of them kinda fleshy-like?

Another question, are Undead and/or Skeletons weak against fire? Cause if they are, then i can just upgrade my weapon to be fiery that might be better.

The upgrade "Of Skeletonslaying" is just a *specialized* upgrade, as far as I'm aware. Undead are undead

.. and that includes skeletons.

Also, in my experience, skeletons are not weak against fire. Some are more "fragile" than others as there are warrior skeletons so to speak and necro skeletons.

Pre-desert undead, do seem to carry a slight weakness to fire, though I'd say somewhere in the 5-10% weakness range, nothing big.

Undead Hounds however are just flat out weak, and just about anything will hit them like a freight train, also you will get some pretty 250+ hits using fire or holy on hounds.