ROME is the rolling edition, designed for individual users.
It is designed to be a working, usable system and will have the most up to date packages.
ROME users should be familiar with the command line or terminal (Konsole) and be able to use it at times.
The Plasma Extended version is basically a complete desktop for most non-technical users. It features software from KDE.org and other Qt based software. It includes software for most day to day tasks.ROME Plasma x86_64
The Slim version of OpenMandriva is for you if you'd like to choose the programs you want to use primarily yourself.
It comes with: the welcome application (OM-Welcome), terminal (Konsole), a file manager (Dolphin), an image viewer (Gwenview), a web browser (Chromium), text editor (Kate, Kwrite), archiving tool (Ark), a graphical program to install packages (Dnfdrake), and of course the well known and feature rich OpenMandriva Control Center.
If you don't wish to have specific software and want a system which has programs for all day to day tasks already installed go with the ROME Plasma full version.