Qtopia is a QT based environment by Trolltech and is the default GUI, running on top of an Embeddix Linux kernel. it is not a Window manager but a complete system which does not use X. For GUI apps to run, they have to be designed for Qtopia. The Cacko QT ROM and tkcROMs are variants of the default Qtopia and kernel supplied.
OPIE is an Open Source project, forked from Qtopia a while back. The OpenZaurus kernel comes with OPIE. Many apps from OPIE will work with Qtopia and vice versa because they are similar.
To run X on Qtopia, you need something called X/Qt. This runs X on top of Qtopia (unsure about OPIE) and any X applications compiled for it. I run GIMP mainly.
If you want to do away with Qtopia (or OPIE), you can have a pure X workstation by installing the pdaXrom. It will not run Qtopia apps but X apps compiled for it, but it makes the Z more like a UNIX laptop.
X/Qt and pdaXrom are not really compatible, but I run pdaXrom GIMP on X/Qt fairly well (one plugin causes a problem).
All these environments are installable by flashing a new ROM, except X/Qt which is a set of packages to install on Qtopia.
I hope this clarifies more than it confuses
;-)