From my experience, "WMS" is the generic term that people use to describe their system. It's an industry-standard term that just means Warehouse Management System, and could refer to any company's implementation of one - Manhattan, Red Prairie, Oracle, etc. We use Manhattan WMOS v2006, but I just refer to it within our company as WMS.
"WMOS" is a more precise term, standing for Warehouse Management for Open Systems, and is the web-based version with the graphical user interface. There's also "WMi", the i-series version, which is the text-based interface that you likely used on your AS400 server. From what you've said, I'm thinking the version you used was WMi v2003r1.
PkMS is the original implementation of Manhattan's WMS, and still provides the backbone to the core functionality for all versions (as far as I know). It stands for Pickticket Management System (I'm assuming they added the "k" in so that the acronym wouldn't be "PMS").
Hope that helped!