Since git is a distributed version control system, the difference is that commit will commit changes to your local repository, whereas push will push changes up to a remote repo.

Does git log local commits?

By default, with no arguments, git log lists the commits made in that repository in reverse chronological order; that is, the most recent commits show up first. ... Useful specifiers for git log --pretty=format lists some of the more useful specifiers that format takes.

Does GitHub count local commits?

Commits are only counted if they are made in the default branch or the gh-pages branch (for repositories with project sites). For more information, see "About GitHub Pages."