Extended desktop is the Windows XP native multi-screen mode, and has issues... like, I don't believe you can expand a window to cover both screens, I'm not positive about that (I have an nVidia card.) I do know that the Windows XP native dualscreen is incapable of having instances of OpenGL on both screens simultaneously, so people who use 3D Studio or Maya or any OpenGL based application (like say a level editor for a game) can only use one screen. I think it also has problems with video, possibly only with overlay, possibly with something else, but sometimes a video that is started on one screen cannot be moved to the other. It's just because windows breaks the screens up into two discrete instances of a "desktop", each with its own resolution etc. and some technologies will not work with that system. It's pretty much exactly the same as having a separate video card for each monitor, one in AGP and one in PCI.
The Spanning Mode creates one "Windows desktop" which is the combined resolution of all screens, so Windows and the applications it runs just see one desktop (instead of several) that is a resolution like 1600x600, or 2560x1024, or 3200x1200 for horizontal, and 1600x2400 or 1280x2048 for vertical spanning. That way, the Microsoft implementation of OpenGL doesn't have to worry about multiple screens because windows doesn't even know there are two monitors. The video card simply renders its images to a single memory space, and the RAMDACs pick two halves of that memory space to create their two monitor signals from.
The only problem with Spanning mode is that the video drivers have to manage applications a little bit, to make it easier for you to use windows without things ending up right in the middle of the break between screens. (kind of hard to read dialog boxes that way.) But I see that as more of a feature, because the tools you get for managing windows in the nVidia NView drivers are much more powerful than the tools in Windows. One hotkey, and an app flies from one screen to the next. Another hotkey, a zoom window pops up allowing me to see the individual pixels something is made of, and click in a region with sub-pixel accuracy. It also supplies multiple desktops, so that you can hit a hotkey or a menu command and go to a different Unix/Linux style work space, I think with the ability to have certain windows be "sticky" too. They've even implemented a way to let you "throw" a window to a desired corner of the screen, by jerk-dragging a title bar and releasing the mouse button while the mouse is still moving, and the window acts as if it's been thrown, traveling until it hits a corner.
Anyway so that's the lowdown on how dualscreen can work in the two systems. Dual-Monitor isn't perfect in either system, both have problems, but at least with nVidia the problems are limited to things occasionally popping up in the middle of the dead zone between screens, and not responding to nView's commands to move over.