One is for the PS version, the other for the plain Z3100 as far as I know. And I doubt you can install one where the other belongs.
I checked it out, and found the following, confusing situation: When I log onto the HP website directly, select my Z3100ps and then the firmware update, I get to the 220.127.116.11 file. But when I click on "upgrade" from my DVD-based user's guide, it takes me to the 18.104.22.168 download, despite the fact that I have the Z3100 ps.
It is just another example of what seems to me to be an attempt to get a product out too fast, without ironing out the bugs. In addition, the technical papers, such as what to do with non-HP media, should be updated at the same time to reflect each new driver and firmware upgrade.
It is sad, because the printer itself is a wonderful product.