I am having trouble determining the difference between MSysGit and Git for Windows. How are they different? Why would I choose one over the other?
(Now) they are the same (as of May 2015 but likely a bit earlier):
"msysgit" and "Git for Windows" have merged under the name "Git for Windows." msysgit.github.io now hosts "Git for Windows" and the main git download site git-scm.com lists msysgit.github.io as the maintained build for windows.
From the updated wiki:
... we decided to just phase out the name "msysGit" (as well as the GitHub org of the same name) and work on Git for Windows (with the corresponding GitHub org, and using the name "Git for Windows" for the installer aimed at "end-users" and "Git for Windows SDK" for the development environment targeting Git for Windows developers).