I don't quite understand. A tag is just a pointer to a commit. Can't you just select the two commits that the tags are pointing to?
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Tags are just named commits. If you are having trouble finding the tags in the graph, you can expand the Tags section on the left, and click a tag name to jump to that location in the log.
Tim's answer is as close as you are going to get using the GUI. What you're looking for may be considered the type of obscure usage that is generally excluded from GUIs to avoid cluttering.
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It's the same as Tim's answer, except each of the selected commits will have a tag beside the description.
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Screen Shot 2016-04-08 at 8.57.22 AM.png
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git diff TAG1 TAG2
You said you can't checkout code, but you need to have the repository cloned somewhere for git diff to work.
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What's the problem with checking out the code? If you currently have any uncommited changes in your sandbox (which you might not be able to commit yet for any reason), you could stash your changes temporarily - and check out the desired version, After comparison you might apply your stash again ...
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