How to update git on Mac OS X Mountain Lion 10.8.4

Hello,

I've learnt that Xcode installs git by default on the Mac. My current
version of git is 1.7.12.4 and it's located in /usr/bin/git.

I wanted to update git to the latest stable version available:
1.8.3.1. I proceeded with the instructions on:
http://git-scm.com/downloads and typed:

git clone https://github.com/git/git.git

(rather than using the .dmg file because I don't want to install a new
version of git in addition to the existing one used by Xcode.
Furthermore, I have no idea where the new version would end up being
installed and I've read that users have had trouble doing this!)

This rendered the following results:
Oliviers-iMac:~ odebroqueville$ git clone https://github.com/git/git.git
Cloning into 'git'...
remote: Counting objects: 157697, done.
remote: Compressing objects: 100% (53116/53116), done.
remote: Total 157697 (delta 114700), reused 143715 (delta 102625)
Receiving objects: 100% (157697/157697), 39.56 MiB | 2.01 MiB/s, done.
Resolving deltas: 100% (114700/114700), done.
Oliviers-iMac:~ odebroqueville$ which git
/usr/bin/git
Oliviers-iMac:~ odebroqueville$ git --version
git version 1.7.12.4 (Apple Git-37)

As you can see, nothing seems to have changed!

Would you have any explanations?

Thank you in advance for your help.
Best regards,
Olivier de Broqueville.