Then tell Eclipse to look for updates: Help > Check for updates.
After the installation, Eclipse will restart and show the old splash screen. Next time you manually stop/start Eclipse it will correctly show the correct splash screen.
If previous releases are anything to go by, then the answer is No. It is best to download the new release, install it, install the latest versions your favourite plugins and point Eclipse at your workspace.
(Common sense says that you should take a backup of your workspace(s) and your original Eclipse installation.)
I've previously tried the "upgrade" path and found that it was slow and didn't give good results.
You can simply download the newer version, then use "File -> Import -> Install -> From Existing Installation" to add all the plugins you had in your previous installation.
Here's a link describing the whole process in details (it says "on Mac Os X", however it should work for other systems as well):