What is the difference between the alternative and desktop cd images?

Yes. The alternate CD comes with all the Ubuntu packages (and so can be used as an upgrade package source by simply running apt-cdrom add). The desktop CD has all those packages already installed as part of the squashfs image, which is convenient for doing new installations, but unusable for doing upgrades with.

The alternate CD installer is not a live CD. You can't use it to try out Ubuntu, test if Ubuntu works or fix a PC/edit partitions without reinstalling.

The alternate CD installer has a command line (curses or similar) installer, whereas the default live CD has a user friendly graphical installer.

The alternate CD can be used to upgrade your Ubuntu version. This is useful for offline computers.

Here you can find information on how to install Ubuntu from the Alternate CD. The Alternate CD provides more advanced installation options than the standard Desktop CD, which is the recommended method of installing Ubuntu. For instructions on how to use the Desktop CD, see the Graphical Install page on the Ubuntu community documentation site.