The 64MB requires OS X 10.6.1, while the 36MB requires OS X 10.5.8. Apple's release notes simply state, "Install this software to take advantage of your Magic Mouse special features."
The Magic Mouse features Apple's Multi-Touch technology, and ships with the , released on October 20. Apple now sells it separately as well for $69.
The Magic Mouse replaced the Mighty Mouse, the name of which Apple was forced to .