$ git diff tag1 tag2
or show log between them:
$ git log tag1..tag2
sometimes it may be convenient to see only the list of files that were changed:
$ git diff tag1 tag2 --stat
and then look at the differences for some particular file:
$ git diff tag1 tag2 -- some/file/name
A tag is only a reference to the latest commit 'on that tag', so that you are doing a diff on the commits between them.