Basically, git commit "records changes to the repository" while git push "updates remote refs along with associated objects". So the first one is used in connection with your local repository, while the latter one is used to interact with a remote repository.

Here is a nice picture from Oliver Steele, that explains the Git model and the commands:

Read more about git push and git pull on Pushing and pulling (the article I referred to first).

Hi, you cannot commit nor push using GitHub CLI.

If you look at gh help, you will see commands related to GitHub Issues, Pull Requests, Releases, and so on. But there are no commands to make commits. This is because GItHub CLI does not replace git.

To commit and push, you can use git on the command-line:

$ git add myfile1.txt myfile2.txt
$ git commit -m "My commit message"
$ git push -u origin HEAD

Building off of @Gavin's answer:

Making lazygit a function instead of an alias allows you to pass it an argument. I have added the following to my .bashrc (or .bash_profile if Mac):

function lazygit() {
    git add .
    git commit -a -m "$1"
    git push
}

This allows you to provide a commit message, such as

lazygit "My commit msg"

You could of course beef this up even more by accepting even more arguments, such as which remote place to push to, or which branch.