git fetch will update only the branch you're on, but not merge any changes in.
Tells your local git to retrieve the latest meta-data info from the original (yet doesn’t do any file transferring. It’s more like just checking to see if there are any changes available)

git pull will update and merge any remote changes of the current branch you're on. This would be the one you use to update a local branch.
In the simplest terms, git pull does a git fetch followed by a git merge

git remote update (Update Project) will update all of your branches set to track remote ones, but not merge any changes in.