In most situations, git fetch should do what you want, which is 'get anything new from the remote repository and put it in your local copy without merging to your local branches'. git fetch --tags does exactly that, except that it doesn't get anything except new tags.
In that sense, git fetch --tags is in no way a superset of git fetch. It is in fact exactly the opposite.
git pull, of course, is nothing but a wrapper for a git fetch <thisrefspec>; git merge. It's recommended that you get used to doing manual git fetching and git mergeing before you make the jump to git pull simply because it helps you understand what git pull is doing in the first place.
That being said, the relationship is exactly the same as with git fetch. git pull is the superset of git pull --tags.