The difference between the various tiling modes in KWin, and how to use them

First of all, a Display Manager (or DM, e.g. xdm, gdm, kdm) is not the same as a Desktop Environment (or DE, e.g. GNOME, KDE, XFCE).

The Display Manager takes care of graphical login, and decides (or lets you choose) what session to run. Or what session*s* in case you choose the "switch user" menu option.

A Desktop Environment is basically a collection of programs (display manager, window manager, session manager, panels, configuration tools, etc.) and libraries (e.g. Gtk) that intend to give a consistent and integrated environment to work in.

A Window Manager manages windows: where to place them, move them, resize them, minimize/maximize them, tile them, etc.). It also handles the shortcuts to do those things. In some cases the window manager also paints the borders of windows, in other cases this task is off-handed to a "window decorator".

The "Run Application" dialog in GNOME is part of gnome-panel, but in another DE it could be another part of the environment.

Who is in charge of painting windows etc. depends; in case there is a "compositor" in use (often part of the window manager, e.g. in Compiz) then the compositor paints the windows on the screen, otherwise (as was usual in the past) it's the X-server doing that.

The Main Menu(s) are put on the screen by a part of gnome-panel, but the data used comes from a bunch of files in /usr/share/applications/ (possibly combined with an equivalent directory in your home for personal changes). Those files have a structure defined by FreeDesktop.org (a platform for different DEs to collaborate on common infrastructure), so that GNOME and KDE know about the same programs (but still can show them differently, and in some cases prioritize "native" programs over "foreign" ones).

And yes, different users can use a different session configuration (and can even define their own ones). In GDM, try the Session drop-down for the available choices.

Furthermore, it is possible to mix & match several components, but that will sometimes result in less cooperation and a loss of "smoothness" in how things work. One very well known example where things get exchanges is of course Compiz, which replaces Metacity if you want fancy desktop effects. But there are lots of other changes possible.

• X11 - a windowing protocol (network transparent by the way) and its implementation (the X server and low level libraries for accessing it). Handles "only" basic input (keyboard, mouse,...) and output (drawing rectangles), but does it in a rather abstract fashion, so that you can run a program on one machine and control it from another one, subscribe to various events etc. There is actually only one usable open-source implementation, namely by the X.org Foundation.

• Qt, GTK, Motif, ... - originally widget libraries, which provide higher level abstraction above the X11 libraries (e.g. creating dialogs, buttons and other graphical elements). However, for example Qt goes way beyond that and has interfaces for a lot of other things as well (databases, multimedia, ...). It also allows for unified design of UI. Similar to what Swing is in Java.

• lxdm, lightdm, gdm, kdm, xdm, ...- display managers: specialized programs that display login screen (some can do it over network as well) and let the user login into his/her preferred desktop environment session.

• compiz, kwin, metacity, xfwm, openbox, ... - window managers: programs supplying basic window environment functionality like drawing decorations to widows (title text and buttons), resizing, moving windows, moving these in the window stack (raising/lowering or tiling them on the screen). They sometimes also handle the "desktop" (background and icons placed on it) as well.

• KDE, Gnome, XFCE, LXDE,... - desktop environments: more or less complete sets of tools. They usually include a window manager, display manager, some sort of "panel" (the thing, where icons, list of currently opened windows, clock, and other stuff is displayed), file manager, multimedia viewer, editor and "goodies" like calendar/reminder, and various desktop extensions)

You can (to some degree) mix applications from different DEs (display managers work fine since they are rather stand-alone however, especially kdm and gdm they pull in a lot of dependencies that their lighter-weight counterparts). The main trouble with mixing apps is that their settings are often intertwined with the DE, and thus may require some services to be running (which are not under the other DE). The look and feel might also be different when another toolkit (e.g. Qt vs. GTK) is used. And that's the redundancy - multiple applications serving the same purpose have their separate and in some sense redundant options.