Well, in the same way that Picasa = Google+ Photos, I guess. Same data, two different interfaces. If you're not a Google+ member, your Google Profile is a seperate thing, on its own site (profiles.google.com). Once you become a Google+ member, these are merged, and your Google Profile URL redirects to your Google+ profile.
The problem is that the Google Profile page has settings which are not available in the Google+ profile settings, such as the ability to change your public profile URL to your Gmail user name or back to the random number string.
EDIT: Here's a screen showing this (using an account I made for a character sharing site, so I don't mind showing it):
http://i.imgur.com/sbcik.png
(Yes, I know it's in Swedish, but you get the idea.)
This setting does not exist in the Google+ profile settings, and can't be reached since trying to view your Google Profile redirects you to your Google+ profile. This account isn't a Google+ member, and therefore I can reach and change this setting. With my real account, I can't.
What I meant was "if you have changed your Google Profile URL from the default string of numbers to your Gmail user name".
Just go to your profile page. There it is.