Git is a version control system. Basically a set of data file standards, network protocols and command-line tools. An alternative would be Mercurial, for example. Both of these are open-source software, developed by a world-wide community and not owned by any particular company.
Github is a website/company/service that allows you to host your git repositories so that you don't have to set up your own server. A competitor would be Bitbucket, for example, run by Atlassian.
SourceTree is a GUI application that you can use to work with git if you don't like the command line tools. It is a piece of software that you install on your computer, and it is made by Atlassian. It can also handle Mercurial repositories.