2h damage questions

I have only attack and 2h generic damage nodes, and am not doing much damage.

On the other build I have, there is one cluster of mace damage, along with some generic 2h damage...the one with the specialization of mace is doing literally 20x more damage with the very same weapon on either build, with the same link setup...

Do you HAVE to pick a weapon specialization to get further damage?

All the increased damage bonuses that apply to a particular damage source just stack together additively.

For example, if I'm using a two-handed mace, hitting something with an area physical damage melee attack like Sweep, and I have no other sources of elemental or chaos damage, then the following are all functionally equivalent:

+15% attack damage
+15% melee damage
+15% area damage
+15% physical damage
+15% physical damage with maces and sceptres
+15% physical damage with two-handed melee weapons

The mace one isn't special, and isn't activating any special bonus. If one of your characters is doing markedly more damage, then there's clearly something different about them beyond which increased damage cluster they picked.

You could consult the wiki article on Damage for a starting point on how this all works (of note: "more damage", which tends to be found on gems rather than the tree, is not the same as "increased damage").

Alternately you could plug your characters into something like Path of Building to look at some calculations, or if you show your characters here maybe someone will take a look.