Well, I think you are using the wrong url in your second case
Try this instead
git clone git@github.com:organisation_name/repo_name.git
The difference is the :
in the url when using git@
vs the /
you are currently using, and the extra .git
at the end.
This should be the same url if you go to github and select the ssh url for cloning (and not the https one selected by default)