Apple Mail Update is a stability update for Apple Mail for Mac. It fixes problems for those experiencing crashes in Mail after updating in OS X 10.5.6.
Apple Mail for Mac is Apple's official mail client for OS X. It's a very competent alternative to Outlook and fits much better into the architecture of OS X.
Apple Mail for Mac is extremely easy to use and features and extremely slick interface. The setup process is extremely easy thanks to the Apple Mail Setup wizard which allows you to configure it to receive just about any kind of mail, including web services such as Hotmail and Gmail.
Note that you can't download Apple Mail as a separate component. It is part of whichever version of OS X you are running and is automatically the default Mail client on your Mac. This download is purely an update for those suffering from stability issues in OS X 10.5.6.
The main problem users have with Mail is when new versions of OS X are released, there are sometimes connections and sending issues that have to be fixed with workarounds although Apple usually issue updates to fix them.
Apple Mail Update may fix stability problems if you've experienced crashes in OS X 10.5.6