According to the official doc of Git, "Git is a free and open-source distributed version control system designed to handle everything from small to very large projects with speed and efficiency"
In other words, git is a distributed peer-peer version control system. In Git, each node in the network is a peer, storing entire repositories which can also act as a multi-node distributed back-ups. Note that there is no specific concept of a central server, although nodes can be head-less or 'bare', taking on a role similar to the central server in centralized version control systems.
On the other hand according to the official doc, "GitHub is a web-based Git repository hosting service, which offers all of the distributed revision control and source code management (SCM) functionality of Git as well as adding its own features."
Also, it can be said that github provides access control and several collaboration features such as wikis, task management, and bug tracking and feature requests for every project.
Github allows you to:
- Share your repositories with others.
- Access other user's repositories.
- Store remote copies of your repositories (GitHub servers) as a backup of the local copies.
I also have to put it out there that you do not need GitHub to use Git.