In the simplest terms, git pull does a git fetch followed by a git merge.
You can do a git fetch at any time to update your remote-tracking branches under refs/remotes/<remote>/. This operation never changes any of your own local branches under refs/heads, and is safe to do without changing your working copy. I have even heard of people running git fetch periodically in a cron job in the background (although I wouldn't recommend doing this).
A git pull is what you would do to bring a local branch up-to-date with its remote version, while also updating your other remote-tracking branches.
From the Git documentation for git pull:
In its default mode,
git pullis shorthand forgit fetchfollowed bygit merge FETCH_HEAD.
