Tags can be deleted and recreated, so they are just like branches and not immutable as some claim.
Same goes for stashes. They are commits which can't be pushed. Stashes could be implemented by creating a new branch and committing both with a generated name.
Am I missing something? Do both things provide more value than they add complexity/things to learn? :)
With the way Stashes are implemented, you don't have to worry about someone accidentally pushing a branch up that was really just some changes they wanted to store temporarily without messing up the repository's history.
With the way Tags are implemented, you don't have to have an agreement with all your colleagues about how a branch should be named to represent a tag. You also don't have to worry about how you have named the branch you're working on that will add support to your current project for it's own concept of tagging.
Stash: A nicer way to store diffs than the filesystem. I could create a new branch, but the same clutter would happen. The stash is also a temporary space. Anything older than a few days is probably irrelevant.
I also use them when I've lost track of the original code and stashing lets me switch back and forth with ease.
I don't use tags.