What is the difference between GitHub and gist?

The main differences between GitHub and gists are in terms of the number of features and user interface:

One is designed with a great number of features and flexibility in mind, which is a good fit for both small and very big projects, while gists are only a good fit for very small projects.

For example, gists do support multi-files, but the interface is very simple, and they're limited in features, so they don't even have a file browser, nor issues, pull requests or wiki. If you don't need to have that, gists are very nice and more discrete. Like the comments, instead of answers, in SO.

Note: Thanks to @Qwerty for the suggestion of making my comment a real answer.

My personal view of Gist and GitHub:

Gist: Gist is a simple way to share code snippets and pastes with others. It is used when you need to share a sample piece of code or technique with your co-workers or friends.

And

GitHub GitHub, on the other hand, provides a platform to share an entire project as a repo among a team (private repo) or to the whole world (public repo).

Both will log version details.

GitHub is the entire site. Gists are a particular service offered on that site, namely code snippets akin to pastebin. However, everything is driven by git revision control, so gists also have complete revision histories.